When I was a baby my parents used terry toweling rectangles that they had to prefold, pin and then cover with a waterproof wrap (that we call pilchers in Australia). These were then soaked in buckets of water, rinsed and then washed and hung out to dry. Later disposable nappies entered the scene and many people abandoned this time-consuming process for the convenience of disposables - creating an enormous amount of land-fill in the process (but apparently using a lot less water, so the jury is out on the environment impact).

Anyway, recently fitted cloth nappies have entered the scene in a big way. These are a massive improvement on the old terry toweling nappies. They are now made from a whole range of materials - from lovely soft bamboo fleece, to hemp fleece and organic cotton. They come prefitted to your baby and they simply snap closed (or are fastened with velcro strips). Inside the nappy many people use a fleece liner to keep their baby nice and dry and then cover the nappy with a waterproof cover made from either PUL fabric or lanolised wool (although some nappies have an inbuilt cover - these are called all-in-ones - more on that later).
What's more you don't have to soak them in water. Instead you simply squirt any solid waste straight into the toilet (with a little hose thingy called a "Little Squirt") and then put them into a sealed bucket until you have enough to wash.
When washing your nappies you just need to remember to have 2 out of 3 inputs in order to ensure that they are properly clean. These three inputs are: detergent, hot water and sunlight. So, if it is going to be overcast for a few days and you won't be able to dry your nappies in the sun, then you should use a hot wash. Otherwise you can do a cold wash or skip the detergent and use washing balls instead. Up to you.
OK, now for your options. Modern cloth nappies generally come in three main categories. You have your "all-in-ones" which either have a removable liner and booster or are "pocket nappies" (containing a pocket at the back to stuff your booster into). Or you have a fitted nappy and a separate cover (pilcher). The all-in-ones tend to come in two or three sizes and so you have to purchase a supply of nappies several times over the life of your baby. In contrast nappies that have a separate cover will often grow with your baby and so you only have to buy a supply once (unless you get a little carried away with trying different brands and buy more anyway...). That said, the all-in-ones will often fit a little better - particularly when your baby is in the tiny newborn stage.
Before Lily was born we decided to purchase a full-time pack of BabyBeeHinds Bamboo Fleece nappies with separate PUL covers (and wool covers for overnight). Afterwards I kind of regretted doing this because it is quite fun to try a few different types of nappies and the all-in-ones are certainly more convenient when you are out and about (and particularly when traveling). Additionally they didn't actually fit Lily properly until she was almost three months old. That said, however, they have proved to be a fantastic buy. Since three months they have totally grown with her and fitted absolutely perfectly. We have never had a leak. They have also worn really well and I have since found out that they are well-known as the "work horse" nappies because they really do last very well.

When Lily was around 7 months old a lovely friend gave us a couple of all-in-one (well all-in-two really) nappies from the fabulous Widdlewuns site (note: actual shop is here). Not only are these the cutest things in the world, but we also found that they were just fantastic for traveling (because packing extra liners, rather than extra nappies takes up so much less space), super quick & easy to put on, and that they dried really quickly. So, we bought a couple more and have just put in a order for some overnight nappies (Snoozywuns).


Other friends of mine have had some success with nappies from Bum Genius (although these did leak apparently after six months on a little one whose mother describes her as a "super wee-er") and Pea Pods (which were lovely a compact on a little one, but then she grew out of them and her parents had to buy more - and chose BabyBeeHinds).
The friend who used Bum Genius also went on to sew her own nappies, which is another great options. There are some instructions and free patterns available to download from Oz Cloth Nappies, which also lists a bunch of online stores that sell supplies (such a PUL, Bamboo Fleece, Hemp fleece etc.).
Unfortunately, all of these nappies are sold by Australian companies and so my recommendations are not much use to people in the USA (where both of the friends of my family-members live). For them I am wondering if anyone out there has any suggestions? (Also, I will email a friend on mine in Ithica who I know uses cloth nappies and update this post with her wisdom).
For more information on cloth nappies (reasons to use, how much money you will save, logistics, why they really aren't that much hassle, etc), here are a few articles:
The Joy of Cloth Diapers
Nappy Tips & folds
How to chose the right cloth diapers
Nappycino (This is not an article - it is actually an online site dedicated to cloth nappies. It has a chat room where you can ask questions of many people who use them and where you can search for past discussions that will probably answer most of your questions.)