ROM Manager is free in the Android Market, but the creators also offer a premium version that has more options and lets you download more ROMs (such as Cyanogen's experimental Nightlies, or Liquid ROMs). You can do everything over the air, which is much more convenient than the manual methods mentioned below. Before you install a mod with ROM Manager, it will ask if you want to use Clockwork to make a full backup. Do so. Each backup will be dated, so you can always go back to older backups if you want. You can--and should--delete older backups if you start running low on space on your SD Card.
Again, it's not entirely cut-and-dried from device to device. To use ROM Manager, folks with the Droid X, Droid 2, or Droid Pro must first use the bootstrap utility (made by the same genius that made ROM Manager). Samsung users must first flash a kernel that is compatible with Clockwork, and so on (a search on the XDA Developers forum will get you headed in the right direction). Since every device is different, do your research on the exact steps for your handset.
In my opinion, one of the most helpful tools out there is the Fix Permissions utility in ROM Manager. Whenever you install a new ROM or update, it's always a good idea to use Fix Permissions. Wait until your apps are all downloaded again (if you've performed a larger upgrade and have wiped) and you're done syncing; then open ROM Manager, scroll down to Utilities, and click Fix Permissions. This procedure can help iron out a lot of force-close issues. It will take around 5 minutes to run, and then it will ask you to reboot the phone, which virtually all custom ROMs allow you to do simply by long-pressing the power button and then selecting Reboot. (No more battery pulls!)
Other Install Methods
You can also download custom ROMs to your computer via the Web, and then use a USB cable to transfer them to the root directory of your phone's SD Card. Afterward, you can boot the phone into recovery--that is, whatever custom recovery you have installed, be it Clockwork, SPRecovery (which was likely installed on your phone when you rooted it), or any other custom recovery. From there you can make a Nandroid backup (a full system/data backup, explained below), and install whatever .zip file you would like (which is how ROMs are packaged).