Samui Airport (USM) has flights via Bangkok (and some international routes), but they can be pricey. A cheaper route is to fly to Surat Thani, then a bus-and-ferry combination. From Pattaya, route via Bangkok.
Getting around
Songthaews circle the ring road, and Grab, taxis and scooter rental fill in. The island is bigger than it looks, so factor in travel time between beaches.