WHITE’S STRATEGY
Perhaps you have heard the proverb Five Groups Might Live But the Sixth Will Die. In 9x9, the proverb is Two Groups Might Live But the Third Will Die. I do not know of any dan-level game where white lived with three groups. Therefore, white may employ one of two strategic choices: (1) live with two groups or (2) make one group as big as black’s group (and komi is your friend). White may switch between these objectives based on the state of the board.
Note: two living groups is not always enough for the win. (If your territory is only two sets of two eyes, you’re not doing very well, obviously.) But the general rule is good enough because in practice it’s hard for black to reduce the territory of both groups at once.
BLACK’S STRATEGY
White’s strategy comes first because black’s strategy is mostly a reaction against the other. Black’s strategy is about balance. On one hand, black strives to stop white from living with the second group. On the other hand, black has to watch that the former group doesn’t wrap around black’s group or grow in size to rival it. Black should win if both objectives are met—white has one living group that is smaller than black’s group.