The goal
We wanted to build a go-kart out of a shopping cart, keep it under $600, and have it running before we graduated.
The build
We found an abandoned shopping cart and made it the basis of the vehicle. Four of us worked on it. I welded the frame and worked out the configuration — where to put the engine, how to tie the cart structure into something that could take drivetrain loads and a rider without folding.
Power came from a 202 cc Harbor Freight engine. Finished, it does about 35 mph.
Figuring it out as we went
The hard part was not fabrication, it was deciding what the frame should be. None of us had built a vehicle before. My welding experience was the only relevant background any of us had, and welding is a technique, not a design method.
So we iterated, and a lot of it failed before it worked. A shopping cart is built to hold groceries at walking pace, not to carry a drivetrain and a person at 35 mph, and finding out where it needed reinforcement mostly meant finding out where it did not hold.
We drove it at school on the last day of senior year.