If you don’t succeed in capturing an enemy square the first time you attack it, don’t give up. Attack it again as soon as possible, before it has a chance to restore its hit points. In this way you can usually keep chipping away at it until you’ve defeated that square. So long as you keep attacking a square repeatedly you’re likely to succeed eventually, unless you’re fighting a much more powerful nation that can restore its hit points faster than you can eliminate them.
Next: The Combat Stats