The match is divided up into sets. In men's tennis you normally have to get three sets to win. For women it's two.
To win a set you have to win six games - but you also have to get two more games than your opponent.
So you can take the set 6-4, but not 6-5. In that case, you'd continue until someone won 7-5.
If you get to 6-6 first, you play a tiebreak. The first person to get to seven points or more by two clear points wins the tiebreak and the set.
To win a game you need to win four points. But rather than going up from one to four they go in this order: fifteen, thirty, forty, game.
If you are tied on forty-all this is called deuce, and then you have to win by two clear points.