Cloth Diapering 101: An Easy Introduction

There are five basic types of cloth diapers.

A flat diaper is a big, uniformly layered piece of cloth, often a 27-inch square of one layer of cotton.
A prefold diaper is a smaller, rectangular piece of cloth, perhaps 15 inches on a side, with several layers, and thicker in the middle.
A fitted diaper is shaped like a disposable, with elasticized legs and waist, and either snap or Velcro fasteners.
An all-in-one diaper is a fitted diaper with a waterproof outer.
A pocket diaper is a waterproof outer sewn on three sides to a polyester stay-dry inner. The back is open for stuffing with something absorbent.

Flats, prefolds, and fitteds can all be used coverless for breathability, which is an excellent method of preventing diaper rash; but they all need separate covers in order to be waterproof. Covers can be pull-on, Velcro, front-snapping, or side-snapping. Additionally, they can be made from vinyl, nylon, PUL, fleece, or wool.

You may also hear about some of the sub-types of cloth diapers:
A preflat has uniform layers like a flat but is the size of a prefold, with thickness somewhere in between the two.
A contour or shaped diaper is hourglass-shaped but lacks fasteners and elastic. Often there is a doubler built in.
A prefitted has elasticized legs, but no fasteners.
A pocket fitted is a pocket diaper that isn't waterproof, or a fitted diaper with an opening in the back for extra stuffing.
An all-in-two has an absorbent inner that can be detached from the waterproof outer so that the outer can be reused several times between washings.

Diapers can be made from cotton, organic cotton, hemp, bamboo, polyester, or some combination thereof.
Flats and prefolds can be laid in a wrap-style diaper cover, which makes them easy to use, like disposables. Or, to prevent poop leaks, they can be fastened with a Snappi, which is a T-shaped stretchy gadget with claws designed to hold the diaper together without pinning. Dritz pins are popular among folks who do like to pin their diapers.

Wet or breastmilk-only-dirty diapers do not need rinsing. Formula-or-solid-food-dirty diapers can easily be rinsed with a MiniShower or similar diaper sprayer. Store used diapers in a kitchen trash can lined with a reusable pail liner (or a garbage bag). For outings, bring along a small waterproof tote (wet bag) or reuse a plastic grocery bag. Wash every 2 to 3 days. Diapers can be laundered by running them through a cold rinse or short wash with no detergent, followed by a hot, heavy wash with a small amount of detergent and an extra rinse. It is important to make sure all the detergent gets rinsed out, because if it doesn't, the dirt won't all get rinsed out either! They can then be machine dried on hot, or air fluffed in the dryer and then line dried. Covers and pocket diaper outers can dry on top of the dryer. There is no consensus on what makes a good diaper detergent. I recommend trying Country Save first. If it doesn't work, try Tide. A small amount of diluted bleach is O.K. for occasional use, but it should not be used full-strength or on a regular basis.