Madison Cloth Diaper Trial

Set Up: Keep wet bags nearby
I have two wet bags set up in my home: a large wet bag hanging next to the changing table and a small wet bag hanging in my bedroom for night-time changes (my daughter still sleeps in our bedroom at night). I keep a third one, a small one, in the diaper bag for changes outside the home. Wet bags are fabric bags with a waterproof lining. You can store dirty diapers in them without the pee, poo, or smell seeping through.

Changing: Dirty diapers go straight into wet bags
As soon as I take the diaper off my daughter, I throw it in the wet bag. For prefolds, the cover doesn't need to be washed after every use. I generally keep the covers out of the wet bag until I'm doing laundry - at that point I round up all the used ones to throw in the wash. Unless of course there is a really stellar poo, then I'll put the cover in the wet bag right away. For AI2 diapers, I remove the liners right away and throw all parts in the wet bag.
Note that once your child starts eating solids, there will be the additional step of removing the solid poo from the diaper before throwing it in the wet bag. There a couple ways to do this either using liners, a sprayer, or by simply dunking the poopy diaper in the toilet or a bucket. These options might sound gross, but they're really not a big deal - cloth diaper or not, you'll be getting intimate with baby poo.

Laundry: Throw everything in the washer
After 2-3 days, I round up all the wet bags I have filled and empty them into the washer, turning the wet bag inside out as I do so - this goes in the wash as well. I set the washer to hot/cold at the largest, heaviest option, and I turn on the extra rinse cycle. I add detergent as I would to normal laundry (in my case that means a single Tide+Oxi pod).

Drying: Hang it all on the line
I air dry all my diapers. If it's sunny, I hang them on a line in my yard to dry over a few hours. On rainy/wintery days, I hang them on indoor drying racks to dry overnight. In a time crunch I throw everything but the covers and wet bags in the dryer. Air drying supposedly improves absorption, but I haven't noticed this myself. I air dry because I feel like it reduces wear and tear on the diapers and it uses less energy. I air dry a lot of clothes in my home, so it doesn't feel like a burden to do so with diapers. If you aren't used to air drying clothes and feel like it would be a burden, I say go ahead and throw 'em in the dryer! Just be careful with items that have waterproof layers - I recommend always air drying wet bags and the covers for prefolds.