Inside the park, you walk. There are no vehicles on the main trail between El Zaíno and Cabo San Juan, and this is what the park is for. The trail is well-marked, mostly flat near the coast, with a steep climb to the Chairama archaeological site if you extend the route.
Horses can be hired at El Zaíno to carry you or your bags to Canaveral, which saves about an hour on the first section. Many visitors use this for the pack-in, then walk everything else. From Canaveral onward, horses are available for luggage transport but the trail is easy enough without them.
Staying overnight at Cabo San Juan or one of the beach camps means you can explore the far beaches in the early morning before the day-trippers arrive — a significant advantage. The concessionaire Aviatur manages the official overnight accommodations (hammocks, tents, and basic rooms) within the park; book directly through their website.