As Easter Island is part of Chile, visitors from the USA, European Union, Canada and Australia do not need a visa to enter Chile, just a valid passport and flight ticket showing that you will leave the country within 90 days. Visitors from other countries must apply for a visa at their nearest Chilean consulate.
Chile charges an entry fee to citizens from Australia and Mexico if they are entering the country on a flight from Santiago. You can pay with cash or credit card. After payment you will be given a passport stamp as proof of payment. The stamp is valid until the passport expires, except for Australians, for whom the stamp is only good for 90 days.