What can you do for someone that has alcohol poisoning and your waiting for the paramedics?

Protect the airway. Try and keep them awake and their airway clear. If they pass out, or begin to vomit, roll them onto their left side. Avoid giving him/her anything to eat or drink.
Stay with them. As you mentioned, calling for emergency help is first and most important thing to do. While waiting, stay with the person. Try to keep them upright in a sitting position. If they vomit, you do not want them to choke on it-that is probably the most important thing to do while waiting for help to arrive.