Well, there are lot of as in the net about how we can go from DMK Don Muang Airport by bus to pattaya.
I did this trip with an amount of 149 Bhat ONLY.
So what I did was basic thing, I was flying from Phuket to Bangkok and in DMK Airport, I went to the exit level one and from there I got the Bus written A1. which goes to a bus stop called Mo Chit station, remember you need to go to the last stop, which is bus stop.
It cost you 30 Bhat ONLY. get down in the last bus stop, don't worry here you will get every type of food and facility.
From here you can opt for another bus which goes directly to Pattaya. This will cost you around 129 Bhat.
Here you will get the bus, remember it will be out side of the bus stop and you need to wait for few hours as it depends on the time.