Getting to Pattaya comfortably can be a little bit of a challenge. There is an airport, but it is so far from the city that flying there from Bangkok will take much longer than drving there. In the end, about the only practical way of getting to Pattaya is by road, which will generally take around two hours. The cheap road option is by bus, which can be a very easy and convenient way of getting around Thailand. Buses leave Bangkok's Eastern Bus Terminal (Skytrain Ekamai station) on a very frequent schedule. Be sure to get the express bus, operated by Roong Reuang. They take the expressway and make only a couple of stops, at most, between Bangkok and Pattaya.
You can also get a bus to Pattaya directly from the Bangkok Airport. The Airport-Pattaya Bus Service is also operated by Roong Reuang. Buses depart from the airport terminal, on the first floor near doors 7 and 8, and go all the way to Jomtien. On the return trip, buses take you directly to the departure level of the airport. Cost of the trip is 124 Baht (about US$4) in either direction.
The most comfortable way to go is by private transfer service. You can usually arrange this through your Bangkok hotel. If you're staying at a place that has it's own property in Pattaya, and you're staying there as well, they may have a low-cost shared transfer service.
If you really want to travel in style, contact Image Limousine. You won't get a black stretch car, but you will get picked up by a roomy car, or van if requested, in which you'll be greeted by an ice cold bottle of water, the day's newspaper, magazines and other amenities.