[If you don't have a hexboard lying around the house, you might consider going by the Amazon store for the board game Kruzno.]
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:
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).
[repostedd from 2014]