If the person isn't responding and doesn't appear to be breathing, move them to a hard, flat surface (if possible). Put your hands one on top of the other (both palms facing down) and interlock your fingers. Place your hands in the center of the chest (at approximately the level of the nipples) and push hard and fast, letting the chest recoil fully between each compression.
If you're pushing hard enough, you will feel popping and cracking as the bones and cartilage of the rib cage move/dislocate. If you're allowing the chest to recoil back up fully between each compression you really can't push too fast (going too slowly is the far more common failure mode).
There... those are the important bits of adult CPR (for the layperson).
The courses are hours long so that the Red Cross/AHA can justify the fees and sell textbooks.