If you want to drive to Samaná from SD you have the choice of driving through Cotuí (Sánchez Ramírez province) or through Bonao (Monseñor Nouel province). We took and I recommend to take the Bonao route because the road is in better condition that the other one. You start in Santo Domingo and take the Highway 1 towards Bonao/La Vega/Santiago, then when you enter Bonao follow the signs towards San Francisco de Macorís and then towards Nagua and Samaná. The roads are well signed and there are U-turn points if you happen to have passed the exit.
The new highway Santo Domingo - Samaná is done and open to the public as I described on this other tip.
Metro bus company has buses departing from Santo Domingo, I believe, twice a day. Caribe tours has 6 daily departures, 3 in the morning and 3 in the afternoon. These buses stop a few times to pick up or let off passengers. The total traveling time is about 4 hours.
The fare at either bus terminal should be around 200 pesos or 5-6US.
The 2 closest airports to Samaná are El Catey and Arroyo Barril airport. If your flight doesn't arrive there, then there's always Puerto Plata La Unión airport and from there you drive, take a cab or a bus to your hotel.
There's a free shuttle from the hotel to the city, which is quite close. Check out the schedule sheet outside the lobby.