Given I have a toddler at home and time isn't plentiful, I had some main philosophies/goals to achieve in building this bike:

It had to be done for nearly nothing or free
It had to be done with the least of tools - no welding, gluing, riveting, etc.
It had to be built with the least amount of time wasted hunting for parts - so it wasn't built to spec, but rather to a vision of design that fit the materials that were available.
It had to be dis/assembled and stored in seconds.

How to source what you'll need:

Bicycle wheels - Doesn't matter whether they're both fronts, front and back or what have you, as long as they're the same size and they can be whatever size you want. I found mine on a bike heading to the dump b/c it was left in the rain for many years and nobody cared. The wheels still spun and the bearings were good so they worked for me! - make sure you save the nuts on the axles!
2 x electrical box cover plates
Wood for the frame - I had some laying around. Because I had enough materials I went with a trailer width roughly the same diameter of my wheels (26") to achieve optimum stability without going too wide. I used a 2x4 internal frame and external sides of 5/8" x 3.5".
2 x 3" sliding bolt locks - hardware store or a garage sale
2 x Zinc Ubolts that snugly fit around your seat tube - hardware store
2 couplings same thread and size as ubolts - hardware store
A bolt and 2 nuts the same size as the ubolt thread - hardware store
6 - 8' 3/4" EMT - my friend had some laying around but you can pick some up at a construction site dumpster
3" x 1" of thick rubbery or vinyl material to wrap around the seat tube and protect it from damage
12-15 Nails - roofing nails will work and are easy to find if you see a roof getting redone, they just toss those nails around so much!

Tools:

I highly recommend getting your hands on 2 or more C-clamps, they make life so much easier
A drill
A 1" spade or coring bit
A metal drill bit the same size as the bolt on the sliding bolt lock
A metal drill bit the same size as the Ubolts
A metal drill bit the same size as each wheel axle (front is smaller than rear)
A crescent wrench and a socket wrench set (or two crescent wrenches)
Hack saw

How it's built:

It's important to recognize the order this thing is built - that's what makes it easy! If you build it out of order you will end up adding more time to the project trying to measure and fit. The instructions are in the order where it's all custom assembled as the project unfolds.

Step 1: Create the Outside Frame

The frame is an outside box of 2x4 and 5/8"x3.5" - build your box frame to the desired outside width and length of your trailer. Ensure you leave enough room for the wheels to sit in the frame.

Assemble your frame so that the 2x4's are the front/back, and the 5/8"x3.5" sides butt against the ends of the 2x4's - this is structurally important.
Nail, not screw it together, because nails have a higher shear load than screws.

Step 2: Mounting the Wheels

NOTE: The picture shows the frame right-side up with the dropouts facing down, when you make this frame you work with it upside down with the dropouts facing up.

Cut 2 - 2x4's to sit inside the frame and support the other side of each wheel axle.
Put your frame on a table so one side is hanging off the edge just enough to allow you to slide a wheel on the inside of the frame.
Take one of your 2x4's from 1. and put it inside the frame. Move it around so it's on the edge of the table supporting the wheel axle, with the other side of the axle is sitting on the outside frame and the wheel sitting in the air.
Take 2 electrical box cover plates and figure out how much into them you want your axle cut-out to be (I went with 1-1.25") - try dry-fitting them into the frame so you can visualize where the wheel will fit, how much space you'll need for the axle nut and your socket wrench to turn the nut, etc. Ideally you don't want the cutout to stick out too much but you need space to tighten/loosen the nut.
Drill the cover plates with a hole big enough for the axle to slide through, then use a hack saw to cut out the path for the axle to drop in - we'll call these plates "dropouts". Do your best to keep them identical.
Install ONLY ONE dropout in the middle of the inside of the side frame.
Just like in 4., hang your frame off the edge of the table, put your inside 2x4 on the edge of the table and dry fit the wheel into the dropout on the one side, while also dry-fitting your other dropout on the other side. Mark it's location when the wheel looks aligned with the side of the frame, you don't want your wheels toe-ing in or out, you want them both pointed straight.
Install the other dropout on the 2x4 going on the inside of the frame, dry-fit it again and if everything is aligned, then screw the 2x4 in.
Repeat the process from 2. to 8. for the other side of the frame.
Drill a 1" hole in the center of the front and back pieces of the frame - this is where the conduit will slide through
Mount the wheels when done

Step 3: Inserting Your Conduit

First dry-fit the conduit in the hole drilled in the frame from the last step
Estimate the two bends needed to get the conduit lined up with your bicycle seatpost without hitting the back wheel of the bicycle.
Bend it like you Beckham. I didn't have access to a pipe-bender so I had to go old school.
Once you're happy with your conduit, insert it into the frame where you'd like it to sit, mark the pipe ON THE INSIDE of the frame where it is about to go through the hole in the frame. The sliding bolt is supposed to go into the side of the pipe and hold it vertical so identify the side of the pipe where the hole should be drilled.
Drill the hole, then put the pipe back in the frame and dry fit the sliding bolt into the hole on the pipe, while also keeping it flush with the inside of the frame. If you're happy, then install the sliding bolt.
Note whether the bolt is installed on the right or the left side of the pipe. Follow 4. and 5. again for the other sliding bolt mounting, EXCEPT mount the sliding bolt on the OPPOSITE side of the pipe than the first bolt. This ensures the pipe is being held in place on both sides and not just one.

Step 4: Connect the Trailer to Your Bicycle

Take the plate off one of the ubolts and slide it into the pipe - it has to sit in the pipe deep enough so it doesn't flutter around but not so deep that it doesn't pivot on the ubolt. Figure out where the hole in the plate on the inside of the pipe is and drill a hole in the pipe to align with the inside hole.
Put a ubolt through one hole of the plate, then insert the plate into the end of the pipe so the hole on the end is aligned with the hole in the pipe. Insert a bolt and through the hole, the plate and coming out the other side - put a couple nuts on it to hold it in place.
Put your vinyl/rubber wrap around the seat post then slide a ubolt on it. Tighten the ubolt on the seatpost with the provided plate.
Now You should have one ubolt pointing off the bicycle and another ubolt pointing off the conduit. Use your couplings to connect them both and you're done!

Step 5: Opportunities for Improvement

Smaller wheels maybe?
All places where a nut is used need to use a lock-nut otherwise the nuts could come loose and fall off
Maybe use less bulky wood stock for the frame?
Going down hills or hitting the brakes with a heavy load causes the conduit to swivel the ubolt assembly on the seat post - I'm thinking of tightly tying the conduit to the seat post and putting a tennis ball on the end so it doesn't gouge my seat post while it pivots.