Electrical floor heating kits run US$10 to $15 per square foot, but bulk wire only costs $2.50. With the controller, you're still running under $4 a square foot. I have a construction background, but not electrical. Are there any good books out there that takes a novice through the steps of buying just the parts and making one's own?
Just don't. This is clearly the best answer.
If you really want to cheap out perhaps you could buy a complete kit with just one square foot mat, analyze the wire used, and try to source a designated radiant wire of similar dimension and resistance. Then fold and spindle that in a similar way to the mat squares.
Remember your fire insurance likely excludes work done in flagrant violation of the building codes. Use of regular copper wire, while possible, is just not advised.
When wire is used for heating, it is important to ensure either that the wire is of very uniform thickness, or that it is constructed of an alloy whose electrical resistance decreases with heat and fed by a device that will limit current. If those conditions aren't met, the thinner portions of the wire are apt to heat up more than the thicker ones; if resistance increases with temperature, that effect will cause hotter parts of the wire to produce more heat than cooler ones, thus becoming hotter still.
It's possible that ordinary wire may "work", but it may be difficult to ensure that there's no danger of the hottest spots getting unacceptably hot. Wire that is designed for heating must be made more precisely, and is more expensive as a result.