How can I play my steam game on a different computer?

My dad and I both recently bought Skyrim, and I envy the graphics he gets on his computer. So today I logged into steam on his computer under my own username, but when brought the game up it was his character not mine. Is there a way to play with my own character on his computer??How can I play my steam game on a different computer?
yeah its probably looking into the save files where the game is saved and loading dads save file and not yours. You can try to get the save files on his computer and see if it sees the file in game.