Black always goes first, then the players alternate. Black may play any empty intersection, with no restriction on the first move or on later moves.
Black moves first, then White, and the players alternate one stone at a time for the rest of the game. Black can place the first stone on any intersection. There is no required opening move.
Is going first an advantage?
Yes. In freestyle Gomoku, the first player has a real advantage, because Black is always one stone ahead in the race to build threats. With perfect play on a 15 by 15 board, Black can force a win. That is why tournament versions add restrictions for Black, such as Renju, or let White swap sides.
This site plays the simple version with no restrictions, so both players follow the same rules. Opening in the centre at H8 is the usual choice. As White, answer next to Black’s first stone and aim to block early: the strategy guide shows how.
The player who moves first also places the last stone on a full board: Black plays 113 stones and White 112 (see drawn games). The board is described in how big the board is.