If somebody's heart stops pumping, it is known as a cardiac arrest. By learning chest compressions (also known as "hands-only CPR") you can assist somebody in need by delivering oxygen and artificial blood circulation to their body. This can be potentially life saving first aid.
It's super easy to learn hands-only CPR, and you don't need to do any mouth-to-mouth resuscitation. We've found this great video from the UK which demonstrates the technique in less than 2 minutes. Check it out, and practice on a pillow or a friend (warning: if you use a friend you should only mime the compressions to avoid hurting them). You can even sing along to Staying Alive if you want to.