One of the absolute cheapest ways to get a cover is to sew one (or so I've heard). I'm in the process of trying my first one right now.
There are many places online to get free cloth diaper patterns. All you really need to do is google search and print out your favorite. Or, you can always trace a diaper you already have and love (don't forget when tracing near elastic, pull the elastic taught to get the actual measurement of the side!
You should have one layer of PUL (which can be expensive but if you get it on sale from a craft store it can be quite cheap). My first cover will be two layers of PUL, shiny sides facing in. The outer layer can be anything that is polyester (no cotton as it will draw the wet toward it thus making the diaper less waterproof). Make sure your threat is also 100% poly!
Personally, I prefer fold over elastic with a nice wide zigzag stitch around the entire cover. Easiest to deal with and the best fit. However, if you would rather you can always either serge or stitch and turn your cover and case elastic in around the legs and back.
Honestly, I can make about 4 simple diaper covers (depending on the size of the cover you make, how much material you buy, and how much you spend on material) for the price of one from the store. They may not look as pretty but they sure are functional. Baby "S" wears them under her jammies at night so we don't really get to see them anyway!