Getting Started

For the older baby:
24+ diapers (see Types of Diapers for specifics)
6+ Doublers (see Types of Diapers for specifics)
6+ pairs of plastic pants, diaper covers and/or diaper wraps. If using only AIOs, you won't need these.
2 pairs of diaper pins (if using plastic pants with diapers that need to be pinned, if using only AIOs, you won't need these.)
Large diaper pail with tight fitting lid
Wipes

Keeping Baby Dry:
With cloth diapers it is important to change your baby's diaper frequently. It keeps baby's skin dry and healthy, keeps baby comfortable and prevents urine from leaking onto your baby's clothes.

For newborns changing every 11/2-2 hours is recommended. Expect to use around 12 diapers each day.
Older children every 2-3 hours or about 6 diapers.

Traveling With Your Cloth Bottomed Baby:
For trips to the store, park, restaurant, visiting friends etc., I use a large diaper bag and take along one diaper per child for every 3 hours I expect to be out.

Diaper Pail Care:
It is important to regularly clean your diaper pail. It keeps germs and bacteria at bay at prevents smells from accumulating. An easy way to do this is to wash your diaper pail at the same time you wash diapers.
Here is how I wash my diaper pail:
Add 1 cup white distilled vinegar to pail and swish around. I now use vinegar instead of bleach because it kills germs and is much gentler and less smelly than bleach.
Rinse with very hot water.
Carefully empty the water into the toilet.
Air dry, outside in the sun if possible.

Washing Your Diapers
If the diaper is poopy I swish the poop off the diaper in the toilet (diaper dunking) and place it in a "dry pail" until washing day.
A note regarding toilet dunking: DO NOT use any "drop in" toilet cleaner if you are a diaper dunker! The chemicals will eat away at the diapers in a hurry. (Believe me, I learned this the hard way.)

My System

Wash the diapers, diaper covers and plastic pants through the pre-wash cycle using cold water and a normal amount of detergent.

I wash the diapers on the "heavy soil" setting with hot water, detergent and baking soda with 1/2 cup of distilled white vinegar added to the rinse cycle.
The vinegar helps remove the ammonia smell, any excess laundry detergent left behind and works like a fabric softener.

Do not use bleach. It will wear out the diapers faster and can cause diaper rash.
Do not use fabric softener. The fabric softener will reduce the absorbency of the diapers by leaving a waxy residue and can cause diaper rash.

Drying the Diapers
If using a dryer. It is best to follow the manufacturer's washing instructions. If they don't come with instructions, use only the LOW when drying your diaper covers, diaper wraps and plastic pants, or better yet air dry them. Most diaper covers dry quickly and they will hold up a lot better if air dried. Most diapers, excluding AIO, can be dried on HIGH.

Line drying diapers and covers outside helps eliminate stains and the sunshine also sanitizes them.

The Bare Necessities
You may need more or less depending on how often you want to wash diapers.
The diaper numbers here assume you wash diapers every 3 days.

For a newborn:
36+ diapers (see Types of Diapers for specifics)
6+ pairs of plastic pants, diaper covers and/or diaper wraps. If using only AIOs, you won't need these.
2 pairs of diaper pins (if using plastic pants with diapers that need to be pinned. if using only AIOs, you won't need these.)
Large diaper pail with tight fitting lid

Wipes