The goal of MakeBridge is very simple. You try to create a chain from the left to the right and the computer is trying that from the bottom to the top. Whoever first completes such a chain wins.
The game is played at a 13x13 big playfield, which is filled partly (every second square) with O's and X' and you create a chain fragment by moving one O over another adjacent one, but that of course only works when the space between isn't occupied by the computer. And the computer does the same when it is his turn.
You basically have to think in to directions to win the game: creating your chain (it just need to be a connection from somewhere right to somewhere left, how complex it is, is unimportant) and stopping the chain creation of the computer at the same time.