Thanks to Amazon's inefficient packing methods, particularly their love affair with oversize boxes, and my aversion to having to interact with people while I shop we almost always have a more cardboard on hand than I can fit in our recycling bin. When I first considered a project to reuse the cardboard I was going to make some saw horses using theRIAA's method for building cardboard lumber. I don't know how or when this turned into a guitar but it did.
I still used his wheatpaste recipe and the construction method is similar but follows a more traditional method of composite build-up, shaping the plies beforehand and laying up net as opposed to cutting the final shape out of a cured blank.

A disclaimer, of sorts: While this project is not a failure it does need some tweaking. Think of it as an advanced proof of concept. It looks great and I was able to get some sound out of it and show viability but a pretty daft design flaw in the headstock prevented full tension from being applied to the strings. I still show the whole process but at the end I'll point out the failures and discuss how I'm working to fix them. Hopefully I'll be able to strike this through soon when I apply a fix.

Step 1: Materials and Tools

Materials

Corrugated Cardboard (Free) - It should be clean, unbent, and uncoated. Finding pieces large enough for the body is the biggest challenge. If you don't have any around, talk to someone at a store that sells appliances. One refrigerator box is probably enough for the entire project.
Wheatpaste (Free) - A simple mixture of flour, water, and vinegar. 4-to-1 water to flour with a tablespoon of vinegar (as a preservative). Heat and stir until thickened.
Machine Heads ($5 - eBay) - You need a total of 6 pegs, single or connected it doesn't matter.
Bridge/Tailpiece ($8 - eBay) - Make sure you have both a bridge and a tailpiece. The bridge is what the strings pass over at the bottom of the body and the tailpiece holds the strings in place.
6 String Electric Pickup($3 - eBay) - You can make your own with magnet wire and magnets, that was my original plan, but time constraints and the low cost of pre-built units.
Strings ($2 - eBay) - The strings need to be for electric guitars or else the pickup will not work. Synthetic strings will not work.
2x 500k Potentiometers w/ Panel Nuts - For the pickup circuit, one controls volume the other helps control tone as part of a low pass filter.
.022µF Capacitor - The other part of the tone adjustment.
1/4" Mono Audio Jack ($2 - RadioShack)
2x Set Screw Knobs
Wood Glue
Screws

Tools

Utility/Hobby Knife
Brush
Tape
Drill/Bits
Soldering Equipment
Wire Cutters
Tuner - Or tuning forks, or another, tuned, instrument.
Guitar Amplifier - Along with a M/M 1/4" cord.

Step 2: Guitar Design

I've never actually owned a guitar so I was winging it with my design, sort of. I did a bit of research on sizing and found some average sizes for the various parts of the guitar. I set a bounding box for the body at 14" x 21" and used a thickness of 1.75" based on this research. The neck was then sized based on a scale length (playable area) of 25". I then simply, and a bit foolishly, sized the headstock by eye and verified the machine heads would fit when the arrived. I did the initial design and modeling in CATIA and then used 123D Make to develop the ply stencils.
The .zip file contains the CATIA parts and the .stl files used to import into 123D Make.

CBGuitarCAD.zip
Download

Step 3: Layup Design

The process for building individual pieces of the guitar is essentially traditional composite construction where a directional material (the cardboard) is bonded together (laid up) in layers (plies) by a glue or epoxy (the wheatpaste). The cardboard is a unidirectional material where the ply direction is along the corrugation and because of this we can tailor the direction of the plies in different areas to give us strength where we need it.
The most prominent use of this is in the neck which needs to be able to handle the bending moment of strings without buckling or bending, the later of which isn't catastrophic but will cause the guitar to be out of tune. This is accomplished by aligning the plies on edge such that the corrugation runs vertically (when the guitar is on it's back) and the plies run the entire length of the neck.
In the body a mix of 0° and 90° horizontal plies provide good strength under all loads, except compression which should be rare, and allows for screws to be used for securing components.
The .zip file contains the jpg patterns and the 123D Make files.

CBG123dMake.zip
Download

Step 4: Prep Cardboard

The cardboard you use shouldn't be just any cardboard. Try to find heaviest gauge corrugated cardboard that has not already been bent that you can. It should also be as clean as possible for something that has probably traveled across the country in a truck. Before you begin you will also need to remove any tape and shipping label remnants.

Step 5: Cut Plys

Select a pattern sheet generated by 123D and a piece of cardboard and tape the pattern to the cardboard taking special care that the cardboard's ply direction is correct for the selected pattern. Grab a sharp knife and get to work. Take plenty of breaks to stretch your wrist, etc. as there are a lot of plies and CT isn't one of this projects goals.
For the body plies cut any interior cavities first and then trim the periphery. Most pieces required to passes with the knife to break free. On the neck plies cutting all the long cuts on the pattern sheet first and then cutting out each individual ply makes it easier.

Step 6: Layup

The general layup process is fairly simple, if not a little messy. If you haven't made any wheatpaste yet visit THIS page and get it done.

With your wheatpaste and brush at the ready grab the stack of plies, order them upside down, and grab the bottom ply. pour a few small puddles of wheatpaste onto the TOP face of the bottom ply and spread it evenly across the surface. You should only need a relatively thin layer, just make sure that the whole surface is at least visibly wet. Slide that ply clear, but within reach, and grab the next ply. Apply wheatpaste in the same manner as before to the BOTTOM face of the second ply. Flip the ply and place it onto the first ply making sure to align all the edges. Now you can repeat the steps starting with painting the top of the second ply, then bottom of the third and sticking them together until you are out of plies. Do not put paste on the TOP of the last ply. There is one exception: Leave the last few plies of the body off at this point so you can access the compartments for the circuitry.
When you are done with a stack cover it with something flat and rigid, like plywood, and then place a bit of weight on top. I used a stack of four 3/4" particle board pieces as the cover and weight. Leave the parts to cure until the are dry, approximately 24 hours (the weight can be removed if necessary after much less time).

Step 7: Circuit Design and Build

A basic circuit for an electric guitar with volume and tone control is pretty simple. A potentiometer wired to a capacitor provides tone control by acting as a type of low pass filter, removing higher frequencies and another, parallel, pot provides volume control. The circuit is completed on one end by the pickup and the other by a 1/4" audio jack. When building the the circuit you will need to feed the wires for the jack through the body before soldering them into the circuit.

When the circuit is complete the final body plies need to be bonded in place. Drill two holes for the two pots and then attach the plies using the same method as before. Remember to apply pressure to the stack when the last ply is in place. When it is dry you can thread the two panel nuts onto the pots and tighten. Apply wood glue around the output jack to secure it to the body.

Step 8: Component Assembly

These, and all of the other components, are pretty much the cheapest versions I could find. Spending a lot on components seemed counter intuitive when the base structure was made of such a cheap material.

Machine Heads: Select a drill size that will allow the pegs to slip through the headstock. For me that was 1/4". Drill holes for the six pegs in the headstock. If they are grouped on one plate then make sure you measure and mark the center distances. The pegs should be set at slight angle, wider at the base, so that the strings will be spaced evenly when they come across the nut. Finish by attaching the plates to the back of the headstock using whatever methods your heads provide, usually screws.

Pickup: My pickup came with two screws and two tapered springs. By placing the springs below the screw holes in the pickup's body you can adjust the distance between the pickup and the strings. Simply mark the two hole locations through the clearance holes in the pickup, place the springs over the holes, the pickup over the springs, and tighten the screws. We'll adjust the height a little later.

Step 9: Frame Assembly

Now it is time to put the three pieces, headstock, neck, and body, together. Since each piece has already been cured this is called co-bonding. If we had bonded all three pieces together while the plies were still wet and let the whole thing dry at once it would have been called a co-cure.
Before bonding everything I also attached a nut (the part at the to of the neck that the strings touch between the tuning pegs and the bridge), made from the radius of a bent piece of cardboard, to the top of the neck. When the nut is in place it will probably help to file in six evenly spaced notches for the strings.

I bonded the headstock to the neck first and then once the joint had set I attached them both to the body. The process is much simpler than the layup process. Simply apply liberal amounts of wood glue to both surfaces and press them in tight. We use wood glue here instead of wheatpaste because it has superior gap filling properties. You can add clean, fine, sawdust to your wheatpaste to get similar properties out of it.

Step 10: Stringing

When the frame joints are fully cured it's time to move onto the long, slow, moment of truth, stringing. Before we start applying pressure there is a little ground work to lay.
I started by unpackaging the strings and feeding the free ends through the tailpiece/bridge. You can do this after attaching the bridge but it just seemed easier when it wasn't bolted down. Next I measured to mark the point where I wanted the strings cross the bridge, setting the scale length. Once you know the bridge's position, bolt it down. Screws seem to work well in the cardboard, threading and holding like normal. Of course they will pull out easier but they are not the weak point in the system.

With the bridge secured now comes the real test. Start by trimming the strings to about 1.5"-2" past their respective peg. Feed each string, from the center of the headstock, through their pegs, turning the pegs just enough so that the string doesn't slip out. Now begin to slowly apply tension to the strings, starting with the middle two and working out and back and forth. Don't fully tighten on string, work up to the correct tuning. As you apply tension watch the weak points: screws holding the bridge, the joint between the neck and the body, and my shortcoming, the joint between the neck and the headstock (In reality it was entirely the headstock's fault but more on that later). To be honest I wore safety glasses through this part as I've seen a cello string fail catastrophically and I value my depth perception. I recommend you wear some too. When the strings seem to be getting to the proper tension it's time to break out the tuner. With the guitar tuned look at the pickup in relation to the strings. You want it to be close but not close enough that it could touch. Adjust it's height using the two screws that hold it in, the springs should keep it tight to the heads off the screws.
At this point there was going to be a video showing that I did indeed manage to get enough tension on the strings for the amp to pick them up and to show it does indeed sound like a guitar but a sudden and inexplicable SD card corruption wiped them so you'll just have to trust me (thankfully the images were already backed up).

Step 11: Finishing Touches

I did not actually make it to this point but the guitar still needs a couple things. The two must haves (unless you play slide, then just one) are a fingerboard and frets. The fingerboard is simply a flat strip of cardboard glued to the neck. The corrugation should be running perpendicular to the length of the neck. This allows us to use eplunkett's cotter pin frets. Simply slide neck-width cotter pins around the top layer of the fingerboard at each fret position and glue in place. The eyes of the pins should be on the thumb side of the neck.
To determine fret positions measure from where the strings touch the nut to where they touch the bridge. This is the scale length. Take that number and the number of frets you want, 22-24 is pretty standard, and plug them in HERE.

At this point you could also attach a strap if you would like. You may also want to attach knobs to the volume and tone pots as well as mark off some increments. I've chosen not to paint or otherwise cover the cardboard because I set out, not to create a replica of a normal guitar, but to create a unique guitar and I feel showing the raw cardboard is definitely unique. Of course you should feel free to decorate to your hearts content.

Step 12: Play! (Maybe)

If you managed to get everything working then plug in and shred. If something collapsed while stringing then hopefully most of it is salvageable.
For me my oversight was in the ply design of the headstock. For some reason I didn't feel it was necessary to strengthen it against the pull of the strings like I did with the neck. This resulted in it bending while I tried to tension the strings. It just kept detuning to a certain tension that it could handle. In the profile picture you can see it bend towards the strings. There was also an issue with my machine head placements. I didn't give them any angle so the strings were touching as they passed.
I'm working on designing and building a new headstock that will address these issues. It will be a little wider and thicker, have on edge plies, and angled machine heads.
A second minor issue is that due to a bad assumption of ply thickness in 123D Make I had to remove a few plies from the neck which meant the width of the strings, set by the bridge spacing, was greater than that of the neck. (I also dropped a few plies in the body and headstock but those were truly redundant.) I've solved this by adding some plies to the outsides of the neck. Since they are bonded directly to the face of the body this has reduced some of the minor torsion in the neck, especially near the top.

With any luck these will be quick fixes and I'll be able to learn guitar. :D Thanks for reading, please leave a comment or shoot me a PM if you have any questions or comments.