The public cars are easy to spot. They are automobiles with a red sign on top that says Sosua-Puerto Plata. There are many more of them than there are guaguas.
Drivers or their assistant (in case of guaguas) are always on lookout for potential passengers. If you are standing along road looking like you need a ride to Puerto Plata, chances are they will at least toot.
Remember, the public cars have a red sign on top. The guaguas are vans, usually old.
What you don't want is a taxi, unless you want to spend the money. They are usually vans, often cream color, and in better condition than the guaguas.
There are also old, beat up buses. They have a letter of alphabet on a sign mounted in windshield. But they go different directions and you could find yourself on one that bypasses Puerto Plata. The public cars and guaguas will take you to center of city.