What is the best way to get from Pattaya to Koh Phangan?

Taking a trip to Thailand. Couple days in Bangkok, then to Pattaya for 4-5 days and then to a Moon Party in Koh Phangan. What is the best way to travel from Pattaya to Koh Phangan? I've flying but not sure about airlines/airport/cost/time etc. Can anyone offer some advice? Also...If we're going to a Moon Party on a Thursday...Is it ample time to leave on that Thursday morning, or should we go the day before? Thanks