By boat
Boat services depart with great infrequency from La Ceiba and Trujillo. These are cargo barges that makes stops along the coast to sell mechandise to local stores. Ask at the docks.
By land from La Ceiba
First off, you have to get on a chicken bus bound for Tocoa that leaves early in the morning from the bus station in La Ceiba. In Tocoa, there are pickups leaving every morning around 9AM. They gather across the street from the market place by the bus station. All of them will try to sell you a ride in their own pickup, but don't let anyone grab you bag until you have negotiated a fair price. Prices for the 5-6 hours very bumpy pickup ride vary between 300 and 500 lempiras, depending on negotiating skills, luck and if you get to ride inside the car or up back with the merchandice it will be loaded bad. Car robberies are common on this route, make sure to hide credit cards and camera memory sticks as well as your passport in case of bad luck.
The pickup trucks stop in Batalla, which is just across a narrow strait of water from Palacios. From here, you can get a collectivo-boat to take you where you would want to go. Don't pay anymore than 200 lempiras to get to Belen or Raista.
To Las Marias
"Collectivo"Once you are in the Belen-area you can ask around for the next boat heading to Las Marias. With bad luck you might have to wait up to 4 days, but usually there leaves a motorised canoe at least 3 or 4 times a week. The one way "collectivo"-price here should be no more than 800 max, 500 is the common price. It is a bit more expensive to go upriver than down. Making the reverse jurney should cost between 300 and 500 lempiras. Use your negotiating skills without being too rude. It is only fair they charge outsiders a bit more than locals that pay even less than the prices stated here.
"Expresso"If you are short on time and have the money to spend, it might be worth considering hiring a private boat. This will cost between 3000 and 4500 lempiras, is roundfare, and usually includes the 2 or 3 overnight stays that the driver has to do in Las Marias. Most boats can take 4 people.
By air
Regular takeoffs from La Ceiba, in small aircraft. Palacios near the park has a small airstrip. From there you can enter the park by boat or on foot. The airstrip in Las Marias is too short to be used for anything else than emergencies. Both Belen and Puerto Lempira also have airstrips.