Note that different recoveries function differently. For example, in SPRecovery the file you are flashing must be named update.zip, which can create some confusion if you want to flash multiple files, whereas Clockwork is a little more flexible. Different phones also boot into recovery differently. For instance, on the Motorola Droid you power on the handset while holding the "x" key. For other devices, you may need to hold the volume-up key. Search forums for your specific device to learn how to put it into recovery before you start installing anything else (try checking the CyanogenMod Wiki's brief partial list, but be sure to dig deeper). You can switch between different recoveries in ROM Manager (by choosing Flash Alternate Recovery), but note that any backups you made in Clockwork won't be compatible with SPRecovery, and vice versa; it's best to pick one and stick with it (and Clockwork works best with ROM Manager).
ROM Manager also has an option labeled Install ROM from SD Card. Using it is very simple: Click that option, and it will take you to the root directory of the SD Card, where you can choose the file to install. It will give you the chance to make a backup and wipe your data and cache, and then it will boot into recovery and install the ROM.
Backing Up and Wiping Data
Always, always, always make a backup before you install a new ROM. In only about 5 minutes, it will take a full snapshot of your current setup as well as your data and settings (a "Nandroid backup"), which you can restore should something go wrong (or if you just don't like the new ROM). You can restore from a backup directly within ROM Manager, or via your custom recovery. Note that a backup is compatible only with the custom recovery that made it--for instance, you need to be in Clockwork recovery in order to install one of your Clockwork backups, and the same is true with SPRecovery. Clockwork creates backups in the /clockworkmod/backup/ directory on the SD Card (which you'll want to remember for deleting old ones). Once the phone is in recovery mode, you can find the backups under the Nandroid option.