Where are Terminal.app profiles files located?
The original answer is spot on; here's more detail on how to restore everything.

Unless you've exported them from the Profiles window - you'd end up with things called "sweetprofile.terminal" - it's a little complicated.

Make sure the Terminal app is closed. Go to your Library folder, and find the .plist file and .savedState directory:

~/Library/Preferences/com.apple.Terminal.plist
~/Library/Saved Application State/com.apple.Terminal.savedState/*


Rename com.apple.Terminal.plist to com.apple.Terminal.plist.bak, and do the same with the savedState directory. Makes it easy to get stuff working again when something goes wrong, and anyone looking at it knows it's a backup file.

Copy the file and folder from the backup to the same places on your system drive:

/Volumes/bu/Users/you/Library/Preferences/com.apple.Terminal.plist
/Volumes/bu/Users/you/Library/Saved Application State/com.apple.Terminal.savedState/*


Open the Terminal up and it should all be restored.



If you've done a migration or a clean install, your preferences might be messed up. Take a look at the permissions of items in ~/Library/Preferences, and take a look at your backup; same with the Saved Application States. If they aren't correct, Terminal is likely to just overwrite whatever you're trying to restore. So in this case:


Make sure Terminal is closed. Duplicate the .plist file and .savedState directory, and add .bak to the end of the original files.
Assuming the .plist file, .savedState directory, and the files in .savedState have the correct permissions, open them - the ones called "copy," - one at a time, in a plaintext editor.
Open the file from your backup next to what you're restoring, so you'll have com.apple.Terminal.plist next to com.apple.Terminal.plist copy. 
Copy the contents of the file on the backup over to the file on the system - into the file named "copy." 
Do all the files, including the ones inside com.apple.Terminal.savedState, and then remove the word "copy" from the end.
Open Terminal, and you should see all of your profiles. If strange things like windows not opening happen, try going fullscreen and back, and other things like that, and close and open the program again.