Summarize the following:
Statistically, you are more likely to hit a ship if you aim for the center of the board, so start there. The four by four squares in the middle of the board are likely to contain a carrier ship or battleship. Imagine the board as a checkerboard, where half the squares are dark and half are light. Each ship covers at least two squares, meaning every ship must touch a dark square. Therefore, if you fire randomly at only even squares or only odd squares, you will minimize the number of turns you need to hit every ship.  Once you have a hit, you will cease firing randomly and commence targeting the ship in question. To keep track of the light and dark squares, look at your own board and imagine that the diagonal line of squares from the top left corner to the bottom right corner is dark. Imagine the squares from the to right corner to the bottom left corner are light. You can count out from there to ensure each square you're targeting is the right color. If you strike out twice when firing, try firing into a different segment of the board. The chances that you just missed a ship are lower than the chances that you missed by a wide margin.

Summary:
Fire at the center of the board. Use parity to up your chances. Move away when you have two misses in the same segment.