Install the ClockWorkMod Bionic Recovery app found on the Market. This will let you install a useful recovery utility that lets you have all the fun. Top button installs the Recovery utility, bottom button reboots into the Recovery utility. Doesn't get much simpler than that. Once in the Recovery utility, volume up and down moves the selector highlight, and the power button selects what's highlighted.
In CWM Recovery mode...
First, do a backup with CWM to backup your system and data. It may take a while, but it is the insurance you should have prior to mucking around.
On your PC or on you Bionic, download a ROM and save/copy it to your SD Card. I don't remember if it's the internal or the external card, but it's one or the other. CWM only recognizes one.
You did do a backup on your Bionic, right?
Now back in CWM Recovery mode, select the Install .Zip from SD card option, select the ROM, confirm, and sit back and wait. Depending on the ROM, you may need to wipe or format various things like the system partition or the cache, etc. By all means, READ ALL THE INSTRUCTIONS ACCOMPANYING THE ROM.
You did do a backup on your Bionic, right?
Once installed, reboot, and voila! You're now running on a new ROM.
Finally, if things get hosed, reboot into Recovery if you can, and do a restore from the backup you made.
You did do a backup on your Bionic, right?
Things can get very wonky sometimes if you don't follow instructions exactly requiring other recovery methods, so you should probably dig and learn those as well.
You did do a backup on your Bionic, right?
Have fun!