What do you do if a person stops breathing but they still have a pulse?

Clear their airway. Make sure nothing is obstructing their airway and move them on their side. If they still don't breathe return them to their back and start mouth to mouth breathing.
Call 911, then... You or someone nearby should contact 911 asap. If it appears they are chocking, then their mouth should be cleared of any obstruction or vomit.; then they would need the heimlich maneuver (http://www.Youtube.Com/watch?V=kjdpr05zmb4) they may need the “rescue breathing.” component classically taught with cpr. (http://www.Youtube.Com/watch?V=7wq5mup29jq) these recommendations are for adults only.
Rescue breaths... You would call 911 but, while waiting, you would need to do mouth-to-mouth breathing. If you are interested, you could take a CPR class and get trained in this maneuver. The 911 operators can also guide you through the necessary steps once you call them and are waiting for rescue personell to arrive.