See Majorca flights for information on getting from the airport to Palma.
I have never taken a bus or a taxi when I’ve been based in the centre of Palma. It just isn’t worth it. The centre is very compact and easily walkable. However, if needs be, taxis can easily be flagged down (or look out for a blue sign with ‘Taxi’ written in white, in the middle of it), and they have access to parts of the city that many cars do not. www.taxispalmaradio.com is a reputable, English-speaking company that allows you to book online.
A good way of getting orientated is to take route number 50 (the city bus tour), which will take you around all the key sights with the usual hop-on, hop-off policy. A round trip takes about 1 hour and 20 minutes, which gives you some idea of how small Palma really is. Tickets cost 13 euros for adults, 6.50 euros for children until 12, and they are valid for 24 hours. See www.mallorcatour.com.
Several bus routes criss-cross the city. The most useful are number 1 (to the airport) and number 2 (which covers the downtown area). Numbers 15 and 25 will take you out to the beaches of Palma and S’Arenal to the east. For timetables go to www.emtpalma.es/EMTPalma. A different company runs buses out to the west Bay of Palma, and the rest of the island: see www.caib.es, in Spanish and Catalan only, but easy enough to figure out. Standard one-way fares for the Palma area are 1.10 euros, or you can buy a 10-journey pass - available at newspaper kiosks and tobacco shops (estancos) - for 8 euros.
As of April 2010, there is also a new metro system in Palma. The main station is at Plaza Espanya and it then heads out to various suburbs on a loop.