Les Baux-de-Provence has no train station and no bus service worth relying on. You really need a car.
By car: it's 30 km from Arles (about 35 minutes) and 25 km from Saint-Rémy-de-Provence (25 minutes). Parking is on the flat ground below the village — a short walk up to the main gate. There is a charge for parking in summer.
The nearest airport is Marseille Provence (MRS), about 50 km away. From there a hire car is the practical option.