There are as many strategies to playing BattleGrid as there are players. Every one of those beta-testing BattleGrid developed their own methods to reaching the best score possible. Each was as correct as the next. There are however several undisputable techniques to get you started:
Before you can sink a ship, you must find one in that vast ocean. On an empty grid, space random shots equally about. Once the grid is filled with various hits and misses, you can make judgements about where the remaining ships might be hiding. In other words, don't click in a two block opening when the only ship you need to win is a Carrier (four blocks).
Once you have a hit, you must determine direction by making selections around the hit. These should be North, South, East, and West since ships cannot reside on diagonals. When one of these directions hits, you have your boat. Continue in this direction until you miss, then reverse direction to the beyond the first hit. If you have gone as far as you can in both directions and still haven't sunk a ship, you're in luck! It means that your shots have hit the middle of several other ships. This situation comes as a result of poor ship placement by your opponent. Consider this when placing your own ships. The computer players may make this mistake in their own placements.