Cost will vary by neighbourhood and accomodation quality. You can pay anywhere from 3,500 pesos to well over 12,000 pesos. It all depends. You will pay a little more if you want furnished and to live in the areas with a constant source of electricity is also a bit of a premium.
Generally you come down, stay with someone or a hotel for a week and find the apartment then. Very little pre planning is done here when it comes to apartment rentals.
Previous threads and posts have been done about this. Use the search function for additional information.