.: How does a game of Go begin?

A game of Go begins with a go board (the standard size is 19x19 spaces, although 13x13 and 9x9 are used in practice games sometimes.) Players alternate turns placing one stone down on the board of their color, with Black always going first. The object of the game is to obtain "territory" and to stop your opponent from doing so. This is done through enclosing an empty area of the board with your stones. You can capture your opponents stones by completely surrounding them (1 or more, it doesn't matter how many as long as you surround them). Captured stones are removed from the board immediately. Any stones of your opponents that you capture are added to the number of territories you have (one captured stone = one added point of territory). The game ends when both players pass on placing a stone.

This is the bare basics of how a game of Go works. For a more in depth (and probably better) introduction to go, please go to Sensei's Library's introduction here.