There are public buses that go from the airport to Palma. If you will be staying in Magalluf Playa de Palma, or Alcudia, there are transfers that you can make from Plaza de España in Palma to these areas. If you are staying for a longer period, say, a week or more, it may be very economical to rent a car on a weekly basis. Taxis are also plentiful but not the cheapest option.