Ideally this route should be done upon entering San Pedro de Atacama because you’re probably arriving from Calama and because it’s a great introduction to the many wild landscapes to come. Nevertheless, the visitors’ center is located at the San Pedro extreme of the route and I think I recall an entry fee.
Just after you leave San Pedro on Ruta 23 and cross Río San Pedro, you will come to a paved spur to the left. Take this until you reach a bifurcation. Stay to your right and you’ll ride right up to the visitors’ center. This is where the dirt starts and it continues until you return to Ruta 23 after almost 18 km. Along the way be prepared for multiple stops and a few short hikes to explore the various natural formations that make Valle de la Luna such a special place.