This isn't the smallest kite in the world, but it's probably the smallest that most people will make.
Add to that the fact that it is made of no specialist materials at all, and you're ready to make a tiny marvel.
(I'll highlight the materials you need as we go along, but you can substitute many other materials at most stages)
Step 1: The Template
This kite is a shape known as a false eddy.
The Eddy kite was revolutionary in its day, the first diamond-shaped kite to fly without a tail, thanks to a unique bagginess to the sail. This version needs a tail because it has a traditionally-taught sail, and has simpler proportions.
The size is not important, but the proportions are. Based on a square, it is trimmed off by one quarter of one diagonal. The shortened diagonal is the centre-line of the kite.
The size of this kite is governed by the spars I used. For no particular reason, I chose to use the bristles from a yard-broom. The bristles were just over 7cm long, which made the basic square 5cm on a side.
I drew the template out on squared paper (the squares are 5mm across) to save the effort of constructing a proper square on plain paper.