Pattaya at around 165km south east of Bangkok, is not too hard to get to, and there are couple of simple ways to get there. Firstly you can catch a local buses, as they depart from the Bangkok eastern bus depot that is easy enough to get to from within the city of Bangkok. It is only a couple of kilometers from the last two stops of the southern Skytrain line, at Ekkamai or Phra Khanong. The only real problem is working out which bus to catch and from what point. There are few English signage at the bus station, with the only English at a couple of the ticketing booths, as generally it is all Thai, and impossible to decipher. If you are prepared to ask around, and you are not carrying a lot of luggage, this is an achievable and cheap transport option, at about 90 Baht.
The other, simpler but more expensive options are either a minibus service, that usually only run from Khao San Rd, or a private transfer, from about 400 bath per seat, or 1100 Baht per vehicle, respectively. It is worth balancing up the number of passengers in your group, and where it is most convenient to be picked up from, when deciding between these two options. Either is going to cover the distance in 1-2 hours, depending on traffic, a least twice as fast the bus. Also, they will drop you where you want to go in Pattaya, or Jomtien, and, therefore, saving a sawngthaew (locally called Baht bus), or taxi at the other end.