Before the flop, the player to act first is just to the left of the big blind. In the case of three-handed play, that would be the button. After the flop, the small blind acts first as always.
Two cards, known as hole cards, are dealt face down to each player, and then five community cards are dealt face up in three stages. The stages consist of a series of three cards ("the flop"), later an additional single card ("the turn" or "fourth street"), and a final card ("the river" or "fifth street").