Most phones use a custom recovery menu where you can flash ROMs, Themes, Kernals, etc. You can wipe data or cache, make a nandroid backup of your current ROM, restore an older backup you made, wipe battery stats and mount usb storage for easy transfer of files from pc to phone.

In this case, to flash a ROM, you need to download the selected ROM onto your sd card of the phone. It is recommended to place it on the root of the sdcard (mnt/sd) but you can also put it in any folder or create a new folder so you know where the ROM (or theme or kernel) is. Once done, boot into your recovery menu and scroll down to wipe data/factory reset (navigation in recovery is different on all devices) and select it, then select "yes". Back out 1 menu and choose wipe cache parition. Then select "install zip from sd", then select "choose zip". Then navigate to where you placed your ROM. Select the ROM and then choose "yes".. It will run a progress while it installs the ROM. Once it has successfully updated the Operating System to the new ROM you chose you can "reboot system now". Sign in as normal and enjoy your new custom ROM...

A boot loop is when the phone boots up, passes the carrier LOGO splash screen and then runs a continuous looping of the boot animation. If you ever experience this, be patient at first since sometimes it takes 5+ minutes to load a new ROM for the first time but it feels like a boot loop. If you ever get stuck in a factual boot loop, remove your battery and manually boot into recovery (all phones are different for manually doing this). Once there,  wipe data again and format system (this is usually found in advanced/mount system but could be different for you) and then reboot system. If the boot loop continues, you may have gotten a "dirty download" or it's not a compatible ROM for the phone you're on (with all the devices out, many people get confused) so you'll need to boot into recovery and choose either "nandroid" or "back up and restore" and do a full restore of the last nandroid backup you made. This will flash your phone back to the exact same state it was in however long ago you made the nandroid.

A ROM is "Read Only Memory" by acronymn value and it's the core operating system of Android. A stock ROM is the AOSP (android open source project) operating system and a custom ROM is what devs offer and are usually based off of the AOSP git.hub or from CyanogenMOD source. Custom ROMS typically have added features built in that stock ROMS don't offer. Such as, Lockscreen Tweaks, Text and Background color tweaks, built in CPU monitors or OverClocking options, etc.. Some ROMS are loaded with extras and some are Vanilla (no real features, as close to stock as possible) but they all offer something different to the community and the only real way to know "which ROM is the best?" is to try them out for yourself since someone else's opinion might not be the same as your's. We don't have a list of different ROMS because in the last year, we have been wow'd by more than 100 different developers across the board!  

As stated in another FAQ, the "best ROM" is defined per user. What may be my favorite might be the worst ROM you've used so we recommend trying them all and see for yourself. Now, since there are so many devices out there and so many different Android versions to choose from, we recommend that you do a little research on droidforums.net, rootzwiki.com, xdadevelopers.com, droidxforums.net, htcforums.com, etc.. They all have sections per device so locate your device in there and go to the "(your phone)  Development" section and you'll see a list of the ROMS available for your device. Most of the time the dev will explain the install methods they recommend and what to do if you're coming from a different Android version than the ROM is using. Just read thoroughly and make a Nandroid backup before modding your device so you can restore it in the case that someting goes wrong.