To program a light show with your Midi Fighter you need to program each sequence in Ableton's clips like you would a drum loop or melody. Each button on the device receives MIDI back via the same Note message and colours are handled via the Note's Velocity. Each bank has a root note (first button on the lowest row) and goes up in 1 semitone increments until you reach the next bank.
Bank 1: C1
Bank 2: E2
Bank 3: G#3
Bank 4: C5
The attached project file (requires Ableton 9) will give you a good idea of how to achieve this and a preview of it can be seen in the following image.
To setup your MIDI fighter you need to open Live's preferences window and navigate to the MIDI/Sync folder and make sure TRACK is on for both IN and OUT (see attachment). Once that is done go back to the main window and check that your settings match the ones in the following picture.
Note: If colours don't match make sure that the Active Colour for each button is WHITE and Inactive is Black in the MF Utility.