How can I refer to specific hexes on a hex board?
There is no standard way, but as it's a two-dimensional grid you can easily project a coordinate system on it.

You can either go in a 90° angle then every second row or column is offset for one half to the bottom or right.

Or you can go in a 60°/120° angle to have straight lines but that looks unusual (and depending on your starting point can easily go into the negatives).