If your club accidentally hits the ball more than once in one swing, it counts as one stroke and there is no penalty.
What counts as one stroke?
A stroke is a fair strike at the ball with the head of your club. If your club accidentally touches the ball again as you swing, such as a chip that clips it twice, you count the single stroke and play on from where the ball ends up.
What is still not allowed?
You have to strike the ball fairly. Pushing, scraping or scooping the ball is not a fair stroke and breaks the rule. You also can't deliberately hit a ball that is moving, apart from the exceptions the rules list (such as a ball moving in water).
What do I do after a double hit?
Nothing special. Count one stroke, play the ball from where it came to rest, and keep going.
The governing rule is Rule 10.1a.
Local rules
Your league's committee may have local rules that change this. Ask the organizer which ones your league uses.