There's lots of info out there on how to load new ROMs, but not as much info on how to easily get your apps restored with their original settings, etc. Here's how I go about it.
1) Backup your apps + data with Titanium Backup. Pay the extra $1 to get the full version.
2) Place the .zip file of the ROM you want onto the highest level of your SD Card.
3) Boot into recovery
4) Do a Nand Backup from the backup/restore menu. This will allow you to load your Plain Jane (or whatever ROM you're coming from) as it is at the time of backup. It will be exactly the same. You should ALWAYS do this before flashing ANYTHING, even if you aren't changing ROMs. I like to toggle USB at this point from the Recovery menu and rename the backup so I can remember what it is. DO NOT LEAVE SPACES in the name of your backup or you will have trouble restoring it later.
5) Go to wipe menu and do a factory reset and a dalvik cache wipe (some updates to a currently flashed ROM will not require this step)
6) Flash your ROM .zip file from the flash zip from SD Card menu
7) Reboot - This usually takes much longer than a regular reboot.
8) Set up your google, facebook, etc. accounts
9) Go to Market and redownload Titanium backup.
10) Open Titanium backup and hit the menu button
11) Choose batch
12) Run restore missing apps + data. Make sure you restore the app data so you don't have to recustomize all of your apps.
13) Choose the apps you want to restore. As you flash more ROMs, you will have backed up apps that you don't want, so choose only the apps you want (for me usually the apps I downloaded from the market).
14) Let Titanium backup do its thing.
15) If you're running LauncherPro or ADW Launcher, your homescreens will be restored as they were, except the widgets won't work.
16) Delete "problem loading widgets" and add widgets that you had before (only if you're using a home alternative launcher like LauncherPro or ADW Launcher).
17) Set up android mail and other accounts. If you are using K9 mail or some other non-stock email account app, your email accounts will be restored when restoring the app + data.
18) Sit back and enjoy your new ROM!
This is how I do it every time. I guess I do a lot of steps, but it doesn't feel that way. I'm sure there are other ways to do it that may better. But this has worked for me every time.
Adding some tabs to help people find this better through the search function:
Restore apps
Switch ROMs
Load new ROM