Now that you have a hexboard, here's on of many games you can play on it. Hexagonal Reversi is very similar to regular Reversi (which is suspiciously similar to Othello, but that's a subject for another post).
Here are the starting positions:
Each player takes turns placing one of his or her pieces on the board so that at least one row of the opponent's pieces lie between the newly placed piece and another piece already on the board at which point the row of opponent's pieces are replaced with the player's pieces.
This figure above shows the possible initial moves if black goes first (B) or if white goes first (W).