The easiest and fastest way would be to fly. Check the Tropic Air and Maya Island Air Web sites for info on schedules and fares.
You could also take a water taxi/ferry from San Pedro to Belize City and then catch the water taxi from Belize City to Placencia -- the boat runs on Fridays and Sundays.
The cheapest way from Belize City would be by bus, via Dangriga.
Belize First Magazine http://www.turq.com/belizefirst/