As far as I'm aware, you go to an area that's marked as "Respray" on the map and press the windows key. A new window will pop up with different colours and skins for you to pick to respray your vehicle with.
If I recall correctly that was someone joking at the time about a random Civillian who told the Tempest to "stop or your tires will be shot." Because my Shadowplay did not work correctly, I had to ask SPC Jefke to give me his recording and I'll have to wait for him to come online to show any...