There are three airports on Palawan, and choosing the right one will save you a great deal of time.
Puerto Princesa International Airport (PPS) is the main one, served by daily flights from Manila (about 1h 20m), Cebu and Clark on Philippine Airlines, Cebu Pacific and AirAsia. Use this if you are going to the city, the underground river, Honda Bay, Port Barton or the south.
Busuanga (Francisco B. Reyes) Airport (USU) serves Coron, and is about 30 minutes by van from Coron town. It receives several daily flights from Manila and a few from Cebu.
El Nido Airport (ENI), also called Lio Airport, is small and served almost exclusively by AirSwift flights from Manila, Cebu and Clark. Tickets are pricey but it saves the long road or boat journey north from Puerto Princesa.
By sea, the 2GO ferry runs from Manila to Coron and Puerto Princesa (about 30 hours), and a fast catamaran shuttles between Coron and El Nido a couple of times a week (about 4 hours, weather-dependent).
Overland between the airports is slow but cheap: Puerto Princesa to El Nido by van is 6–8 hours along a winding (and now well-paved) road; Puerto Princesa to Port Barton, about 4 hours.