Dynamism is at the heart of King's Indian attack (like many other openings). You cannot be fixed on always going for the kingside or alway going for the queenside. You have to be flexible with respect to all options including kingside, queenside, both sides or center conflict. Also bear in mind that it is a modern opening after all. So, regarding center and general plans, it shares traits of many other modern openings (see chapter 6 of Fine's book "The ideas behind chess openings" for instance). But, beware: the theory of modern openings have changed from its inception (esp. with respect to importance of center).
In some variations, you can strike back at the center in better circumstances than the opening (timing is important for this). Sometimes, you can even push the e4 pawn to e5 (this opportunity doesn't come often. This push will simply loss the pawn (and center dreams) more often). When the center is kind-of fixed, the typical pawn-structure advises white to go for a kingside attack, and black to go for a queenside attack.
See section C of exeterchessclub's openings page for a short overview. For more detailed one, read chapter 7 of "Winning chess openings" (extra read: 1st para. of chapter 5 of the same book).