NiMH's have replaced NiCads as the rechargeable battery of choice, because they have a higher capacity than NiCads and don't have the special disposal requirements that NiCads do. You can get AA's from Thomas Distributing (800-821-2769) for as little as $1.25 each. If you need them today, you can get a pair of AA's at Radio Shack for $9.99.
Unlike NiCads, NiMH's contain no toxic metals and have no special disposal requirements, so when they won't hold a charge any more you can throw them away. If you prefer, many manufacturers will recycle the batteries if you send them back. (e.g., Duracell, 1-800-551-2355 to get the address)
Note that NiMH's come in different capacities; for example, one D-cell might be 2200mAh while another is 8000mAh. So always check the label to see the capacity. If the capacity isn't stated, don't buy it. Of course, you'll pay more for higher-capacity batteries. Thomas Distributing has a good assortment of NiMH sizes, and they clearly state the different capacities. Note that some chargers may not completely fill up a high capacity NiMH D.
A possible downside shared by both NiMH's and NiCads is that they put out less voltage than alkalines (1.2 V instead of 1.5 V). That means that devices which require four or more batteries might not even work at all with NiCads or NiMH's. (They might work; it depends on the device. Doesn't hurt to try. Appliances that take only one or two batteries usually work fine. Four batteries, maybe, and eight, probably not.)
Unlike alkalines which lose their voltage steadily, NiMH batteries maintain most of their voltage over the whole charge and then suddenly plummet, as shown in the graphs below.
For this reason many electronic devices that tell you how much battery life is left have a hard time reporting an accurate level for NiMH's. The voltage is very similar for both a fully-charged battery and a nearly-spent battery. Some devices (like my GPS wristwatch) let you specify in the setup menu whether you're using NiMH or alkalines, so they can try to be more accurate with the battery-remaining indicator.
Another downside of both NiMH's and NiCads is that they self-discharge quickly (~20-25%/month). Self-discharge means they lose power even if they're just sitting in a drawer. Shelf life is about 2-3 months. So they're not the best choice for, say, emergency flashlights (use alkaline instead) or smoke detectors (use lithium -- lasts 7-10 years).
You can't recharge NiMH batteries in an old NiCd charger. If you try the batteries could explode. If your charger isn't specifically labeled as handling NiMH batteries, then it can't.
How to charge. You'll get more recharge cycles if you charge soon (before the battery has lost too much power). But since you can typically charge NiMH's hundreds or thousands of times even if mostly drained each time, you probably shouldn't worry about it, and can just charge recharge whenever you like. Just try not to drain the battery completely before you recharge.