This is the cheapest way to go to Pattaya and as long as you don't have a lot of baggages its a comfortable way too.
Leave the airport by
Gate 10 and look out for the SHUTTEL BUS Booth.
The Shuttle Bus will carry you (FREE of charge!) to the Suvarnabhumi Bus Terminal. There is a Bus to Pattaya Jomtien at 09:00, 13:00, 17:00 and 20:00. Should you stay in Pattaya or in Naklua but not in Jomtien, tell it to the Bus Driver.

This (Yellow) Bus Line doesn't stop at Pattaya's Bus Terminal! It runs the Sukhumvit Road only.
The price we had to pay at the time of writing was 106 Baht only.
Bell Transport has a direct Bus from Airport to the Pattaya Bus Terminal. The one way ticket is 150 Baht. For this Bus please contact the ATTA Counter on Level 2 (Arrival Hall) or phone the Bell office (02 747 4675, 02 747 4676). The bus is waiting at level 1 (Bus Lobby), at door 7. The Bus to Pattaya leaves the Airport at 08:00, 10:00, 12:00, 14:00, 16:00 and 18:00.
On the Ground Floor (Level 1 called by the AOT, short for Airport Authority of Thailand) there are Busses connecting the Airport with Tourist Spots of Bangkok.