Taxis, trying to find a taxi here is not easy, lucky there is plenty of busses and the city is relatively small, you can go anywhere in the city within an hour walk. There are taxis, but only in three or four taxi stations in the city. At lunch time most of them are gone and at night only a few of them work. So if you are comming to murcia be ready to wait for the bus or get confortable shoes.
Latbus is the company that provides the public transport for the Murcian region. You never have to wait very long for the next bus. Its not expensive and most of the time busses are on time and they take you everywhere in the Murcian region.
Avery easy and comfortable way to travel to Murcia is by bus. Spain has a whole network of bus lines that connect all the cities and even smaller places. One of the bus companies that provide this service is ALSA.