Build in dimensions that are multiples of 4 or 8 to take advantage of using full sheets of plywood, for example. Fewer cuts, less waste.
Consider using pallet wood for some things. There's an entire thread on pallet projects.
Metal roofing is probably cheaper than plywood and shingles.
Let friends and neighbors know what you're doing, if you have a good relationship. A neighbor asked me if I wanted the metal frame that is now my run. She "just wanted that junk out out of there!"
Check the reject bin (or whatever it's called) at Menards, Lowes, etc. If there are commercial building sites around, ask if you can go through their scrap pile. But don't make a mess, obviously.