If you are not using a hire car you have the choice of public transport or taxi. The taxi rank is just outside Arrivals, however if you are staying in the north of the Island you will be better off pre-booking a local taxi from Puerto Pollensa itself as it will be cheaper and your driver will know where he is going.
If you choose to use public transport, which is incredibly cheap, take the Airport Bus which can be caught from a stop at the end of the taxi rank. These buses run to Palma every 15 minutes. If you are not staying in the city or the port you will need to get off the bus at the Plaza d’Espanya. From here go down the steps past the train departures to the bus station which is used by the red and yellow TIB buses. These buses have luggage compartments and the 340 bus to Puerto Pollensa takes just over one hour and costs only 6€. It usually leaves from bay 14 and allows you to soak up the fantastic scenery along the way. The journey ends at the main roundabout near the taxi rank in Puerto Pollensa.
There are two train stations at the Plaza d’ Espanya, the one at the bus station which goes to Inca and the well known Soller tourist train a few minutes walk away. Taking the train to Soller is a wonderful experience with great views of the countryside and takes an hour and 10 minutes with a few minutes stop on the way. When you get to Soller there is a tram to and from the Port de Soller operating every 30 minutes and this shouldn’t be missed! Make sure before you go you plan your journey from the available timetables, which are seasonal, with summer starting on May 1st.