On Linux Mint 11, you do this by opening "Keyboard" from the Control Center. Open the Layouts tab, click Options, and assign the key you want to "Compose key position". On Linux Mint 12, you open "Keyboad Layout" from the System Settings. The rest of the steps are the same.
Your key + a diacritic will combine the diacritic with the next letter typed. For example to get é, you press your key + ' (no character appears on the screen), release both those keys, and press e. If you want ê, you first press and hold shift, then your key + 6, release all three keys, and press e.