Hi,
You have a few options:
Into Bangkok and then;
Minibus from Victory Monument, about 250Bht (could be less)
Train to Hua Hin (google the train times though - you may have to book a seat)
From Airport;
Fly to Hua Hin (depends where you stay or you may not get a seat)
Taxi to Hua Hin (from memory 2 to 3000 bht) - you should be able to arrange from here.
One of the best options is to ask your accommodation in Hua Hin to recommend.
The journey by road is about 2 1/2 hours.
We usually have a couple of nights in Bangkok and arrange transport while we are there.
One tip - unless you are dealing with a known and reputable company, do NOT pay in advance (by card or whatever means requested) for transport - there are some transfer rip off merchants about!
Cheers
Peter