Which player gets the first turn of the game can be determined in a number of different ways. Normally both players roll a D6 and the player with the highest score can decide to move first or second (first being a popular choice unless you have a really cunning plan). Sometimes the kind of game you are fighting will decide it for you. For example, in an ambush the attacking side will always get the first turn.
Fighting all sorts of different battles is covered in more detail in the Battles Book.