Each player starts with a blank grid, on which they place a number of ships. Usually five ships are used, with each taking up 2-5 squares on the grid. Each player takes turns taking shots, by calling out the coordinates of the square they wish to attack. The other player must call out whether the shot was a hit or miss.
The paper version of the game has two 10 by 10 grids placed side by side on a single sheet of paper. The left grid is used to record the position of each of "your" ships, as well as the locations of all "shots" fired by your opponent. The right grid is used to record the locations of all "shots" you fire, along with the results of each one (hit on a particular type of boat, or miss).
When recording hits, players may wish to fill in the letters A for Aircraft Carrier (5 consecutive spaces), B for Battleship (4 spaces), C for Cruiser (3 spaces), and S for Submarine (2 spaces). When recording a miss, place a large X in the square to indicate it is empty.