Battleship is a game of both luck and strategy. To tip the scales toward strategy, it helps to play an offensive game.
You can increase your odds by firing with purpose, even when you're firing blindly (which is the vast majority of the time). Select a pattern to consistently follow on the grid, either aiming at every other space horizontally, vertically or diagonally. This allows you to cover the most ground across your opponent's board, and you're bound to hit a ship sooner or later. Once you do, you can fire at the coordinates immediately adjacent to your original hit until you get another hit and see a pattern emerge.
And, because each ship takes up a specific number of spaces, you can begin to narrow down what ships remain as the game progresses. For example, if you've already sunk your opponent's patrol boat, carrier, destroyer and submarine, scan your board's top grid for four-space openings in which a battleship could fit -- and aim there.
Most opponents will expect you to place your ships in a variety of horizontal or vertical positions. Occasionally, if you place all your ships in the same direction -- vertically, for example -- you'll leave your opponent guessing because he's likely to assume that they're in both positions. This also means he'll need to fire more shots to actually hit them.
And, although it may seem counterintuitive to group two or three of your ships close together rather than spreading them out across the grid, it's an unusual move that could throw off an opponent. Most players will assume that your ships will be spread throughout the board, so after hitting and sinking one ship, they'll begin calling out coordinates in other regions of the grid. This could give you valuable time to call out a hit or two of your own.
Alternatively, it can help to insulate the battleships on your own board by keeping at least one empty space all around them -- that way, your opponent will have more spaces to guess after getting the first hit on each ship. If you place a ship along the edge of the grid, you're giving your opponent a better chance of taking your ship down quickly.