You can build a great kite from black plastic trash bags (the big yardwaste kind) and duct tape--just requires some careful cutting and taping. Outline the shape you want with chalk or something, and cut carefully. Straight edges are best, so I use a metal ruler and an exacto knife.
You want multiple layers, so it's best to cut one side, tape that, and it'll keep things together. Tape the edges by pulling out an equal length of tape, laying it with the edge you're taping lined up with the tape strip's center, and folding it over. Saves weight.
Create some pockets at the corners for the sticks (small dowels) with more tape, use some kite string to make hookup points for the line, and you're good.
If you want, you can also make a tail out of surveyor's ribbon or something like that.
I've built some bat-winged double line kites with this process that flew great--every bit as good as the really expensive nylon and fiberglass-stick stunt kites, at least as far as I cared. They didn't cost me an arm and a leg, either. :)