Swipe to move the tiles, when two tiles with the same number touch, they merge into one.
When a 2048 tile is created, the player wins.
You have a limited number of free squares, and each move introduces another tile into the mix. But combine like numbers into their sum and you've opened up the board for the new tile and simultaneously progressed a little further toward your goal of making a magic 2048 one, a feat accomplished by combining two 128's into a 256 and two 256's into a 512 and so on.