This is the most basic, and cheap option to cloth diapering: A prefold and a snappi with a cover:
How to do our favorite fold, the angel wing fold (the green wash cloth is just to cover baby parts for the photo!):
Here is another fold you can use. This is called the bikini twist and is a bit more complicated:
This is the jelly roll fold. It works well for containing newborn poo!
This is the easiest fold, and is great for babies once they are older and the poo is a little less runny!
These are a few folds we have tried. I'm sure there are others as well. Prefolds are great because they are virtually indestructible. They are also cheap. You can get a dozen for as little as $18. I prefer the unbleached versions, but bleached is fine, too. There is little difference between Indian and Chinese in my opinion as well.
One thing I will mention is there are lots of sizes of prefolds. They make a preemie size, newborn, infant, baby, toddler - you'll see tons of different terms. Preemie prefolds are generally quite small and thin. They work well in the beginning for tiny babies (think twins), but newborns of normal size are best in a newborn prefold. Infant sized will work, but you may have to fold down the back or front to have them not be so high up on baby.
My favorite prefolds are Green Mountain Diaper prefolds. We used the orange edge newborns in the beginning, and they lasted us until about 3 months or 10lbs. I now use the yellow edge Green Mountain Diaper prefolds and Tiny Tush infant prefolds on Claire at 4 months. They fit perfect without having to fold down. Green Mountain Diaper makes prefolds in lots of different sizes. Some of mine were bought used, and they held up really well.
You can have an entire stash of prefolds and covers to diaper from birth to potty training for under $200. It's quite economical, and you can wash and dry them hundreds of times and they'll still be in perfect shape!