The transport infrastructure in Mallorca is very good. If you want to explore the island by bus or train it will certainly help if you are based in Palma.
The hub of the islands transportation network is based in the Plaza España, from here you can reach any part of the island. There is a bus that runs from the Airport directly to the Plaza España, connecting you to your final destination.
Maybe you would even like to travel by ferry to Ibiza or Menorca, while on you stay in Mallorca.
There are various forms of transport available
EMT
These are the local buses (blue & silver) that will transport you within Palma and its outskirts.
Prices - 1.25 Euro for all journeys (you do not need to explain where you are going, you can just get on a bus and just say uno (1) or dos (2) and the bus driver will charge you 1.25 or 2.50 accordingly.
The only exception is the trip to and from the Airport which costs 2 Euros
Link to a Map of Palma including all EMT bus routes (save a copy by right clicking over the link and selecting "save as"
Link to a EMT bus timetable (save a copy by right clicking over the link and selecting "save as"
TIB
This covers all buses serving the island (red & yellow), connecting town to town. TIB also covers the Trains, which connect Palma to the north of the island.
Link to latest TIB bus timetables
Link to latest TIB train timetables
Train to Soller
This is the famous electric train that travels from Palma to the town of Soller, through the impressive Tramuntana mountain range.
Link to the Train to Soller website
Link to latest timetable and prices
Boat
Sometimes it is difficult to see something big when you are too close, some of the boat cruises provide a way of stepping back to take in the whole view.
Metro
The new metro (Underground) has recently opened in Palma, which travels between the Plaza Espana and the university.
Ferries
Link to Acciona-Trasmediterranea ferries where you can book online your trip. Remember that in the height of the summer you can not usually just turn up as they will be full.