As far as eating affordably as a vegan goes, I don’t think it is different than any other lifestyle. The same general principals apply:
1. Start off with basic ingredients and make things yourself whenever you can.
2. Learn the prices of the things you buy at the stores near you.
There are a bazillion money saving tips, but I think that these two ideas alone will produce 85% of the value.
This is a fun topic so feel free to add all of your money saving tips in the comments.