Just stand by the side of the road and when you see a beat up car, usually red with a sign on the top flag it down. It will stop. Just get in. The price is about 40rd from Cabarete. At the road to the airport just tell him to stop and get out. The walk is not too far from the road.
There are vans also. Most are white with a crazy Dominican hanging out the door, these are a little less money, but will take you.
If you are in doubt just look for a Dominican by the side of the road waiting and do what they do. Chances are they are waiting for a Publico.