Step 1: Obtain parts and tools
1/2" conduit bender
punch (or nail)
1/8" bit and 3/8"
half round file
oxy-acetylene torch or arc welder
plentiful brass brazing rod
brazing flux. goggles, and gloves
bricks for holding frame
framing square / "L" layout tool
Finding and Buying Parts
You can find a lot of the parts, particularly if you're near a metal dumpster or a building renovation that might be ripping out conduit. Metal shops often have scraps of flat stock that you might be able to take.
Wheels: Go with what you can find. Feel lucky if you have the option of mountain bike wheels over road bike wheels. The dimensions given here are for carts with 26", 27", or 700c wheels. If you use 24" wheels, you can reduce the cart depth by 1", and if you use 20" wheels reduce the dimensions by 3" (spine and ribs dimensions). 700c and 27" wheels work, but ther're less strong, particularly laterally, which is important when you're hauling a load around corners.
Find wheels at bike shops or in the dumpsters out back. I've had good luck asking bike shops for old wheels, and in college metal recycling dumpsters. Make sure you get 2 of the same diameter, with the diameters within 1/2" or so with the tires on. You can get tubes with small punctures behind bike shops.
Another wheel possibility: It's easiest to use 2 front wheels because they will have the same hub spacing. However, you can use a front wheel and a rear wheel if you make one of the wheel wells longer and increase the hub spacing for the rear wheel to 4 3/4", instead of 4". Or measure your wheels exactly. Hardware stores carry the EMT conduit and hardware.
You will save some money if you can find scrap 3/16" by 1" bar, plywood and 3/8" ID tubing. Try metal dumpsters, scrap bins at machine shops and mechanics' garages, etc.
In the store, hardware parts are generally less expensive in the bulk bins than in pre-packaged boxes. I can't find rod end ball joints anywhere accept mail order (I've used McMaster-Carr). The shaft should be 1 1/4" or more, and have threads that are 3/8"-24 or 3/8"-16. (The 24 and 16 refer to threads per inch.) Get a nut to match the threads. The hole through the ball should be 3/8" wide. You can order it from mcmaster.com. It is part 6072K64 for the oil-impregnated bronze race with a chrome plated steel ball and right hand threads. It costs $5.92 without shipping. I think shipping is $3 or $4. You might consider getting a welding respirator ($12) from McMaster-Carr at the same time.
For plywood, ask at a lumber yard if they have scrap wood. Building renovations and construction also generate waste plywood that will work fine.
Using the tools
To use a conduit bender, line up your bend mark with the arrow on the bender. Step on the foot plate, while pushing down and pulling sideways on the handle of the bender. Bend until the bubble level reads level with no force on the handle.
Working with metal in this project is easy, but takes some practice. To cut with a hacksaw, make sure the piece is clamped well and the cut is close to the clamp. Use the full length of the blade, pushing down hard enough to cut but not hard enough to bind the blade. Use steady, even strokes pushing forward. Don't press down hard on the return stroke. Hold both the back and front of the saw.
When using files, the cutting happens on the forward stroke. Pulling back with downward pressure on the file will only dull the file.
To cut with a tube cutter, align the mark with the cutting wheel and tighten the screw just enough to score the metal all the way around the tube. Tighten a little more and continue turning the tool, ensuring that the cut is in the original groove. Continue around the tube. This tool is useful for the conduit, but a hacksaw is more reliable.
To braze with an oxy-acetylene torch, it's a good idea to get a lesson from someone who knows how. Always set the regulator carefully and keep the tanks well secured so they could not fall. Use gloves, #5 shade eye protection, and work on non-combustible surfaces. Keep fire-extinguishing paraphernalia present. Work with good ventilation, especially with galvanized conduit.
To drill into metal, make a starting dent with a punch or nail, and drill a small hole at high speed with a sharp metal bit. To enlarge it, use a lower speed and watch out for the bit catching as it breaks through the material. Always drill into material secured in a vice or by clamps.
General safety: Wear gloves when things are hot, don't wear gloves with spinning tools. Wear safety glasses when there are chips flying (drilling, cutting). Wear long non-synthetic, non-flammable clothes when working with the torch. Wear closed-toe shoes or boots. Don't breathe fumes from cutting, heating, or painting. Have fun and take care of yourself so you can ride your bike and pull your bike cart and tell your friends how great it is to not use a car.