How can I find Terminal.app manually? I believe that I moved it somewhere using a command line like this:
sudo mv Terminal.app ./Desktop
It didn't show up on my desktop, and it isn't in Applications anywhere
If that's the command you typed, terminal is now named 'Desktop' and is still in your /Applications/Utilities folder (since you would have had to be in that folder for the command to do anything at all).
Take a look in there for stray Desktops :)
Terminal is in /Applications/Utilities/ by default.
If you actually moved it, try typing Terminal in the Spotlight menu and pressing ⌘↩ (command-return). (If ⌘↩ doesn't do anything, it's probably because of the Apple Events bug in 10.8.2.)
If even that doesn't work, try running this in AppleScript Editor: