If you hit a ball that isn't yours, you add two penalty strokes in stroke play, and the shots with the wrong ball don't count. In match play you lose the hole. You have to go back and play your own ball before teeing off on the next hole.
What do I do in stroke play?
Take the two-stroke penalty, then continue with your own ball, either where it lies or by taking relief if the Rules allow it. Strokes made with the wrong ball, and any penalty strokes you got from that ball, are wiped from your score.
If you don't correct the mistake before you hit off the next tee, or before you return your scorecard on the last hole, you are disqualified.
What about match play?
You lose the hole. If you and your opponent swapped balls, the first one to hit the wrong ball loses the hole. If nobody knows who hit first, there is no penalty and you finish the hole with the balls swapped.
What if someone hits my ball?
If it is known or virtually certain that another player played your ball, you put your ball, or another one, back on the spot where it was. You don't get a penalty.
How can I avoid it?
Put an identifying mark on your ball, and say which ball you are playing when others are using the same brand and number.
Any exception?
If you hit a wrong ball that is moving in water, in a penalty area or in temporary water, there is no penalty, but the shot doesn't count and you have to fix it.
The governing rule is Rule 6.3.
Local rules
Your league's committee may have local rules that change this. Ask the organizer which ones your league uses.