I made an 8' Folding Kayak for around $100 based on plans by Jess E. Rathburn originally published in Popular Mechanics in 1963. The plans have been modified by multiple people and instructions are available online for free in various locations:

http://www.vintageprojects.com/boats/folding-kayak.pdf (original plans)
http://www.ida.net/users/tetonsl/kayak/
http://www.vhcbsa.org/camping/kayak.pdf
http://www.duckworksmagazine.com/00/DM1999/articles/foldingkayak/index.htm

I've attempted to gather the most helpful tips and modification from each set of plans.

The kayak is made of plywood and canvas, and is bonded together with contact cement. The entire boat is coated in latex primer and paint, which waterproofs it. It folds up for easy storage, and is relatively easy to carry short distances.

Step 1: Gather and Prepare Materials

These are the materials you will need to make one kayak:

2 - 1/4" 4' x 8' Sheets Untreated Plywood, smooth on one side
1 piece wood lath
1" x 2" wood for seat support rails (about 2' - 3')
Exterior Latex Primer
Exterior Latex Paint
200" Heavy Canvas, untreated
Waterproof Wood Glue
2 - 2" Screws and Matching Nuts
Heavy Duty Velcro
Contact Cement (the strong stuff that creates fumes that will explode without good ventilation!)
6 or more - "C" Clamps

One of the sheets of plywood must be cut into four 1' x 8' pieces, the home improvement store will likely make these cuts for you for free if you ask.

Step 2: Cut the Wood, Paint the Interior

One of the sheets of plywood must be cut into 4 - 1' x 8' pieces.

Clamp two of the pieces together (good sides of the wood touching) to cut the cockpit opening. The cockpit opening should start around 41" from the front of the kayak, and can be whatever shape you'd like. The cut should have a depth of about 5", and be about 28" long. See the attached photograph.

Now you get to decide what your kayak will look like. Clamp all four pieces of wood together; clamping the wood together will ensure your cuts match and the kayak is symmetrical. Round the edges of the kayak creating whatever shape you'd like. Don't make the front and back too pointy, or it will be hard to attach the canvas later. We left two inches flat on each side. See the attached photos for a better explanation.

Tape the wood where indicated in the second photo, wood strips will be installed here, and will attach to unpainted wood more securely. Prime the inside of the kayak with a exterior latex primer.

Paint the inside of the kayak with at least two coats of a flexible exterior latex paint. Porch and Floor Exterior Paint worked well, and was in the cheap-o mis-mixed color table for $5.

Step 3: Make Spacers and Spreaders

2 Spreaders
Cut 4 - 11" x 24" pieces of 1/4" plywood. Each spreader will consist of two 1/4" pieces of plywood bonded together. Using wood glue and "C"-clamps, bond the wood, creating two 1/2" thick rectangles.

Cut the spreaders to the dimensions specified on the attached photograph. The center of the spreaders can be cut out to reduce weight.

2 Spacers
The spacers will be used to hold the kayak pieces together and in the correct configuration during application of the edge canvas. Scrap wood can be used to make these.

Cut 2 - 3" x 3" pieces of plywood (dimensions are critical).

Cut 4 - 2" x 6" pieces of plywood (size of these is not as important).

Drill a hole through the center of all pieces of wood. Sandwich the 3" x 3" pieces of wood between two of the 2" x 6" pieces, attach with 2" screw and matching nut.

Step 4: Prepare the Canvas, Cut and Assemble Kayak

The kayak will be assembled using 5 strips of canvas of the following dimensions:

2 - 4.5" x 46"
2 - 4.5" x 72"
1 - 13' x 12" (this may vary, don't cut this one until step 6)

Draw outlines of the strips on the canvas. Paint the canvas with two layers of contact cement, allowing cement to dry between applications, before cutting. Applying the contact cement before cutting will prevent the edges from fraying.

Assemble the kayak with the spacer blocks according the the attached photo. Draw a line 2" inches in from the edge, all the way around the kayak. Apply two coats of contact cement to the 2" marked border, allowing to dry between applications. Repeat on the bottom of the boat.

Apply canvas strips using the 2" marked line as a guide. The shorter strips are applied to the front and back of the boat, the longer strips on the sides. Stretch the canvas, and apply slowly, smoothing wrinkles as you go. After each strip has been fully applied to one side, flip the kayak over and apply the remaining canvas to the bottom.

The strips will overlap, apply contact cement on the canvas where the overlap occurs, and secure.

This is the most difficult part of the kayak assembly, it requires patience. This step is easier with two people.

Allow to dry for at least several hours before installing the spreaders.

Step 5: Install Stop Blocks

Eight stop blocks will hold each spreader board in place. The spreader board will pop into place between the stop block.

Cut 16 stops blocks from wood lath. Mine are about 1.5" x 1.5".

Determine where you would like your spreader boards to be positioned by installing them and getting in your kayak. I installed mine 22" from the front of the kayak and 22" from the rear, giving me enough room to sit with my legs extended.

Install stop blocks using waterproof wood glue. These will be installed on the unpainted sections of the inside of the kayak.

Step 6: Install Center Canvas

Install the spreader boards. Measure the largest gaps, at the front and end of the cockpit. This will determine how wide your center canvas strip will be.

You should add 4" to the largest gap to allow for at least two inches of canvas glued to the wood on each side. The strip will be approximately 13' long.

After you cut your strip out , center the strip and clamp it onto the kayak. Mark the canvas at the front and back of the kayak. Taper the canvas in these two spots to match the width of the front and back of the kayak. See attached photo.

Install the canvas with clamps again, and draw an outline around the canvas on the kayak. This will be your guide for contact cement application.

Apply two layers of contact cement to both the canvas and the kayak, and apply starting at either the front or the back.

Step 7: Assemble and Install the Seat and Seat Rails

The seat consists of two pieces of plywood, joined with a canvas hinge. The seat sits on 2 rails that are glued to floor of the kayak. The seat is attached to the kayak with velcro.

Cut two rails from 1" x 2" piece of wood, mine are about 17" long. Attach these to the floor of the kayak on the unpainted sections.

Cut two plywood rectangles for the seat. Determine the size of each piece with the spreaders installed in the kayak. Measure the distance between the seat rails to determine the width.

Cut out a small piece of canvas to use as a hinge, attach the two pieces of wood together. Paint and prime.

After the kayak and the seat have been painted attach velcro to the seat and the rails.