This trailer was built over time, with a couple of iterations. A few times in this Instructable, I'll use the phrase, "Ask me how I know..." Most of these lessons were discovered during failures of the trailer on the road... these were cases when "the wheels coming off," is more than a figurative phrase.
Also, I make no claim that my solutions to these problems are the best or only way of solving them. However, in the spirit of Instructables being "open-source hardware," feel free to choose, mix, and match these solutions to your favor.
Step 1: Overview & Anatomy
Main body: the body of the trailer is a plastic bin with a lid; I used an Akro-Mils Nest & Stack Tote (NST) Model 35300 (29 1/2 x 19 1/2 x15)--I bought mine at Grainger. I like it because it is pretty intrinsically strong and stiff. However, I think this plan can be adapted to most plastic bins.
Wheel mounts: the wheels are mounted to metal brackets on the sides of the container. They are adapted from brackets from Home Depot, with some cutting and drilling.
Internal Structure: the plastic bin is not strong enough to support the wheels (ask me how I know), so an internal frame is needed to hold everything together. It connects the wheels to the bin, and the bin to the trailer connection.
Hitch (trailer side): to connect to the rear wheel hub, the hitch needs to take a right angle and come in at roughly 45 degrees to the axis of travel. Therefore, when you make a turn in one direction, the hitch comes in roughly parallel to the rear wheel. There is a flexible coupling (rubber tubing) to allow turning. The connection to the rear wheel is made using an air hose quick-connect.
Hitch (bicycle side): the connection to the rear wheel to the trailer is made out of a metal bracket with an angle that matches the hitch, which remains semi-permanently in place on the bicycle (you can remove it, but you will need a wrench). It doesn't add much weight, so I leave it on all the time.