As Tom Vidrine explained, there are NO ferries from Playa del Carmen/Cozumel to San Pedro (Coz is just off the coast from Playa). You take a ferry for the short trip from Coz to Playa. Last year I think I paid about US$7. Then you can take a bus (deluxe or first class, with reserved seats, videos, etc.) from there to Chetumul (around US$10 and 6 hours). Then you can take a Belize bus across the border to Corozal Town (about a dollar) or Belize City (a few bucks), and then a ferry (US$12.50) to San Pedro. Or you can fly from Corozal to San Pedro, or you can fly from Coz or Cancun to Chetumal or to Belize City. Unfortunately there is no easy & cheap & fast way to do all this.
Eventually, as there is more integration between Belize and the Yucatan/Quintano Roo, there will be ferry service or more flights, but this is probably some years off.
Belize First Magazine http://www.turq.com/belizefirst/