Before I talk about anything else diaper-related, I added links to photos to the first cloth diapering post so you could see what each type of diaper looks like. Note that I'm not specifically endorsing any of these sites, but tried to cover a wide variety so you could see how many resources were out there. Poke around on these sites--there are some wonderful products out there.
About prefolds: You can't buy diaper-service quality prefolds at regular baby stores (BRU, BBB, and other big box retailers). All you'll be able to find there are the cheap Gerber prefolds, which are thin and not that absorbant, and are really only good for burp rags. To buy good absorbant prefolds you'll have to go to the internet.
Actually, you'll probably have to go to the internet to buy all your cloth diapers. There are hundreds of choices, so read reviews and maybe only order one or two of each kind until you know for sure you like it. (If you make diapers and want to pimp yourself in the comments, go ahead--I think it will let people know about options they don't already know about. Just put your URL in so when people click on your name it'll come up. I know I don't have to say it, but if anyone abuses the intent of the comments I'll just remove their comment.)
About diaper pails: You'll want some sort of pail with a lid. I use a big plastic wastebasket with a foot pedal. You could probably start out with a pail like the Diaper Champ when your baby's diapers are tiny, but once your baby starts to grow and the diapers get bigger, they might get stuck in the champ's lid. It's probably easier to stick with a plain pail with a regular lid.
You'll also need some kind of bag to line the pail with. You could use kitchen or large garbage bags (but they rip and get wasteful, since you can only use each one once or twice). You could use regular laundry bag, but it would leak into the pail and you'd have to clean out the pail every time you did a load. Or you could spend money to buy one or two PUL drawstring bags to line the pail with. I have two and they are the best investment I've made in cloth diapering. (I spent $12 apiece on them 3 1/2 years ago. It looks like they're up to $13 per now.)
I don't know anyone who uses a wet pail system (although I'm sure someone will delurk to say she does!). I just toss the diapers in the PUL bag inside the pail. For poop, if it's breastmilk poop from a young baby I just toss that in because it's liquid anyway. For a baby eating solids but without formed poop, I swish a little to get off the chunks before I toss in the bag (now that I'm using pocket diapers this is super-simple). (Or you can buy one of a number of gadgets that lets you spray the poop into the toilet.) For a baby with formed poops I roll them off into the toilet and then toss into the pail. Since I only wash once a week (more about that below) the bag can get kind of ripe, so I make sure it's drawstringed closed--the smell is horrendous while I'm tossing in a diaper, but once the bag is closed I can't smell anything. (The smell was never bad back when I used to wash every 2-3 days.)
About washing routines: There are as many washing routines as there are cloth diaper users. I'll share mine, then you share yours. (If you have a good routine for a special situation, like hard water or soft water, I'll put your comment up in the body of the post so everyone can read it as part of the original post.)
This is my routine for exclusively pocket diapers with a mixture of hemp and microfiber stuffers. My routine was slightly different back when I was using prefold and fitteds with covers.
I have a shared washer in my building, so I don't have the ability to control cycles on the machine. If I did, I might add a cold water soak to the front of my routine, and I'm sure I'd add a hot water rinse to the end of my routine.
I fill the machine with hot water and add half the recommended amount of washing detergent*.
[Here's my #1 laundry tip in general: Always use half the recommended amount of detergent. The detergent actually traps the dirt on the clothes, and if it doesn't get rinsed out, neither does the dirt. If you can still smell a strong detergent smell when your clothes are washed, you've basically covered up the dirt with perfume, much like the French did back in the 1700s when they only took baths every few months. (I apologize if you're reading this at lunch.) Put your clothes through a cycle with no detergent whatsoever and there's probably enough left in them to wash them perfectly. If your diapers ever stink even after they come right out of the machine, run them through again with no detergent, and from then on use half of the amount you've been using.]
Once the machine is full, I flip the bag full of diapers inside out into the machine, and toss the bag in, too. I let the machine go the full cycle. Then I hang my diapers and covers (and the bag) to dry. (Since the stuffers aren't touching my baby's butt, it doesn't matter if they're stiff from hanging dry, but sometimes I still think they feel a little stiff so the next time I'll add in a Downy ball of white vinegar to go in the rinse water.)
When the diapers are dry I stuff the stuffers back into the pockets. The end. Repeat the next week.
A typical routine for a younger baby (under 3 months, say) using prefolds and PUL wraps (like Prowraps or Bummis) would be to wash every 2-3 days (figuring you'd go through 8-10 diapers a day at that age). I'd do the exact same washing routine, except that I'd have sprayed each poop diaper with Bac-Out enzymatic stain treater before I tossed it in the diaper pail. Once the wash cycle was done, I'd hang the covers and bag to dry and put the diapers through a dryer cycle. (If one dryer cycle doesn't completely dry your diapers, throw in a clean dry bath towel and they'll dry fully.) If I had any poop stains on my diapers I'd hang them out in the sun to get the stains to disappear. Never use chlorine bleach on your diapers, as they'll get holey pretty quickly.
* I use Tide Free or Seventh Generation. For my clothes I use Ecover or Mrs. Meyers, but they leave a slight residue on the diapers that makes them water-resistant because they have a vegetable base. It makes my clothes nice and soft, but isn't what I want in a diaper. Some people love All Free & Clear for diapers, but I found that they left a serious residue on my pocket diapers, rendering them mostly water-resistant after only a few washes (I think it's the "stain-guard" stuff in the AFC). Another detergent cloth diapering people like is Bi-O-Kleen, which I've never used.
Now I need to know how you wash. Or what your questions are. Or what kind of diapers or covers you make, and where we can buy them. Or what kinds of diapers you love (and whether your kid is skinny or chubby).
[If you want to know my all-time favorites of the diapers I've used, my favorite non-pocket diaper was the fitted hemp diaper from Crickett's Diapers. It was the most absorbant diaper I've ever used. My favorite AIO was a snuggly hemp fleece inner/waterproof fleece outer I bought new from a WAHM on Ebay. My favorite pocket diaper is an Angel Luvs I got new from Ebay with a PUL red tie-dye print on the outside and super-soft red fleece on the inside--I love it for the softness of the fleece, nothing else. Note that I haven't tried a bumGenius yet, which is supposed to blow all the other pocket diapers out of the water. My kids have both been extremely chubby in the thighs.]