Tips on General Care
Most importantly: Be nice to your battery! Don't do anything to it that you wouldn't want done to you. Don't drop or shake the batteries, and don't expose them to extreme temperatures. If you're carrying replacement batteries with you, then store them deep in your bag as opposed to the outside compartments, so that they won't be as exposed to jostling and temperature changes.
When not in use, keep your rechargeable batteries in a cool, dry place. However, try not to leave batteries in storage for long periods of time. If possible, use them at least once every 2-3 weeks.
If the contacts on the batteries are dirty, gently clean them with a cleaning solution (which you can make yourself) and a cotton swab. This will allow the most efficient discharge of power from the battery to the camera as possible.
All rechargeable batteries, no matter how new or expensive, have a limited number of possible charges, and the duration of those charges inevitably decrease over time. Thus, the fewer times you have to charge them, the longer the batteries will last. Practice good power-saving techniques. On your digital camera, run the LCD brightness at the lowest light level you can, and try not to leave the camera on for extended periods of time.
When you first purchase new rechargeable batteries, they (should) arrive in a discharged state, which means you'll need to charge them first thing. Furthermore, they won't reach their maximum capacity until they're charged and discharged several times. Some people will thus "tone" their batteries by charging and discharging them a few times before actually using them out in the field.
Also, make sure both the charger and the camera are calibrated to the discharge pattern of the particular battery - for batteries and battery charges purchased from the same camera company, this shouldn't be an issue, use of off-brands and DIY projects does not have this same guarantee.
When the lifetime of your rechargeable batteries is done, don't forget to recycle! All rechargeable batteries contain compounds toxic to the environment, and so need to be taken care of in special facilities.
Care also differs slightly depending on the type of rechargeable battery you use: