They will either use a larger needle after creating a disinfected field around it to prevent introducing bacteria. If it contains thick material they will probably have to lance it and scrape it out and possibly suture it closed. Worst case senario they will cut around it to remove the cyst and its capsule and suture it back up under sedation or anesthesia. They may follow up with antibiotics. Since I haven't seen it and I'm not a vet this is all a guess. Be sure to get a written estimate and discuss the possibilities with your vet.