OK, let me explain. The Rom is basically the OS. You technically cannot have multiple ROMs installed at the same time although I've seen some topics about dual booting and the like, but you don't really need that.
There is an option to do a nandroid backup (will get back to this in a bit) which basically allows you to restore your phone to a specific 'screenshot' and so in 2-3 mins you can have different roms up and running, but really that's something you'd look into after you get used to the whole thing.
So here is what happens. I personally don't have a Desire (my roommate does) and back then when we did it the first time rooting was incredibly hard. Since then he somehow managed to fuck up his ROM and we had to revert back to an original Rom and redo the whole rooting process. This just involved flashing a shipped rom (i.e. a proper official HTC rom) and then rerooting. The second time was incredibly easy with unrevoked. What happens is that you basically get superuser permissions on your phone, allowing you to edit and change system files.
In most cases, the actual rooting process installs a recovery image. With your phone as is now (don't worry this is just a demonstration), shut it down, and start it back up while holding the volume down button. You should boot into a white screen. That's the Hboot menu. From there you can select between fastboot or recovery both of which have different purposes. What happens is that when you root (using unrevoked) you install an alternate recovery image. From there you can perform several administrative tasks, such as factory wipe, backup (the aforementioned nandroid backup) as well as flash update.zip files.
Update.zip files are basically a signed zip which contains some update and a script to install it. Traditionally the had to be called update.zip, these days the recovery image allows you to select any zip file from within the root of the SD card.
All you will need to do is get one of these updates (the biggest being full Roms, the smallest being themes and fonts and the like) put them in the root folder of the SD card. Boot into HBoot, select recovery. This boots you into the custom recovery image which is installed on root. From there you will then have to perform a nandroid backup (safety first :]) then most probably a full wipe (factory reset, wipe dalvik-cache, wipe ext partition) and then select apply update.zip (all this is within this recovery menu). For added comfort, it allows you to mount the SD card to your pc to transfer stuff etc. Now, warning, the first time after a wipe it takes aaaages to boot. Trust me, just wait (it may take 20-30 mins at times). And then you're done, with a custom rom
Yes, Cyanogen is a Rom too. It is however built from actual android source code and not the code HTC released for their own phone. Strictly speaking the only difference you'll immediately feel is the absence of HTC sense but as you can probably tell from the Android Customization thread is that with LauncherPro or ADW Launcher you can get the same and even better experience than with HTC Sense.
Again I suggest you take it in baby steps. Fist just root. It's pretty quick and painless. Once that's done chill out for a bit and check that you can properly boot in recovery.
After those steps are done just let me know and we'll walk through it together
Edit: So we're clear, you do not need to root to install LauncherPro or ADW Launcher.
Edit2: This is shit-ton-loads more clear than all the crap I said up there:
http://forum.xda-developers.com/showthread.php?t=788044
