This is a fairly simple idea, albeit implemented in a relatively complicated fashion. Two players compete, via the magic of the interweb (or a local network), in a full-scale sea battle. Players place ships of varying sizes in a grid and then take it in turns to try and blow up the other's (hidden) fleet, one shot at a time.
Weapons available are: missile - a standard one-shot one-square ballistic; cluster bomb - like 9 missiles in a 3x3 grid; heat seeker - automatically hits the nearest in range vessel-square; radar - scans a 3x3 region and reports how many enemy vessels were found. Players have only 2 cluster bombs and 1 heat seeker in their arsenal per game.
In order to play the game, players should arrange for one to be the host, and the other to be the client. The host starts Battleships and selects the 'host...' option, along with a port number (the default one should be okay), and presses 'Go'. The client then starts Battleships and selects the 'connect to...' option, and inputs the host's IP address and the port number they selected. Finding out your IP address or port-forwarding (etc) is a little beyond the scope of this page, but neither is overly tricky with a bit of a google. Once the client presses 'Go', Battleships should connect, and the game begins.
Placing ships is done with the left mouse button. Changing their orientation is done with the right mouse button. Each player must place 5 ships of lengths 5, 4, 3, 3, and 2.
Once ships have been placed, firing commences. Select your weapon from the options on the right, and then click on the grid. If you are viewing hostile waters (red), you take your go where you click. If you are viewing friendly waters (blue), you are taken to the hostile waters screen (also available via the options on the right) where you can select your co-ordinates.
There's are other little bits and bobs, but they can be left as exciting undocumented features for you to find. Imagine your wonder when you stumble across how to start a new game (with mutual concent)! Gosh, you've got it all to look forward to, haven't you?
Finally, 'cos this was written in Delphi, a long time ago, it's only runs in Windows.
battleships.zip - Zip file containing Windows executable and icons.bmp