Unlike chess, which is a complex game that has spawned hundreds of books on strategy, the strategy for Battleship is not very complicated. Basically, there are only two simple decisions in your Battleship game. First, you have to figure out where to hide your ships, and then you have to figure out how to shoot at your opponent's board.
Placing Your Ships
The object of placing your ships on the board is to make your opponent take as long as possible before finding all of them. On the most basic level, this means that your ships should be placed somewhat randomly. All other placement guidelines are based on considerations of how your opponent is likely to attack.
Do not place your ships touching each other: An opponent who scores a hit on your grid will likely circle that point looking for the rest of the ship. If your opponent finds two ships at once, then you have just lost an extra ship.
Place a ship on the edge of the board: Many opponents will fire most of their shots towards the middle of the board, so having at least one ship on an edge may give you an advantage. Do not place all your ships on the edge, or your opponent may guess the pattern of what you are doing.
Be asymmetrical: In other words, do not mirror your ship placements. If you have a ship one square away from both edges in the lower left, do not do the same thing in the upper right. The human mind seeks patterns, so your opponent will be more likely to find both ships after finding the first one.
Be unpredictable: If you have followed the above rules for a few games in a row against the same opponent, then break them. This will confuse your opponent and ensure you are not too easy to outguess.
Taking Your Shots
The goal of your shot-firing is to locate and sink your opponent's ships as quickly as possible. Unless you are a mind-reader whose random guesses are likely to hit, you should go about firing your shots in a logical and ordered fashion.
Guess in diagonal lines: In other words, if your first shot is fired at C-1, consider firing your next shot at F-4, and your next shot at I-7. By firing shots along a diagonal line, you guarantee that each of your shots is located in a new row, and a new column, thus maximizing the number of rows and columns into which you are firing.
Do not bunch up your shots early on: Your initial goal is to cover as much ground as possible, so do not start by firing shots adjacent to each other, even diagonally. Instead, leave a few spaces between shots. After your opening salvo, you can go back and fill in the gaps in your diagonal lines. Once you have fired enough shots to draw a few diagonal lines, you will notice that you have used those lines to divide the board up into small chunks. From this point forward, you should try to systematically take shots in each chunk to eliminate the possibility of your opponent's biggest remaining ship existing in that region.
Consider the checkerboard method: If you imagine the firing grid as a giant checkerboard, with alternating white and black squares, you can hit all opposing ships by firing only on black squares. This meshes well with the diagonal line strategy and means you never need fire on half the squares in the game (the "white" ones) except to finish sinking a ship you have already hit. When you score a hit, continue to fire adjacent shots to attempt to continue sinking the opposing boat.