Airports:
Murcia (RMU) - just over 15mins drive (directions here), serviced from the UK by Low Cost Airlines (Ryanair/Jet2/Easyjet) seasonally.
Alicante (ALC) - just over 60mins drive (directions here), serviced by most European airlines (flights available all year round).
Airport Taxi:
Taxis from Murcia are about 25 euros each way and are normally available from outside the airport terminal.
Train:
The national trains (Renfe) are available to Balsicas-Mar Menor, a few miles from the resort. See Trainline for details.