Marbella does not have an airport, but there are two large airports not far away, one in Malaga and one in Gibraltar, so it's best to check for the cheapest flights before you decide, although Malaga is by far the closest.
Hiring a car in Marbella is probably the easiest way to get to your hotel, but taxis are also available. Hotels and package holidays will often include a transfer from the airport, so do check. A regional bus service that runs from both airports along the coast to Marbella, although often very busy in the summer and the service can be sporadic in the winter. In addition there is a shuttle bus direct from Malaga to Marbella. The bus station in Marbella is about one km from the beach. Although there are some Marbella hotels in this area, you're likely to have to take another local bus to your final destination.
Most of Marbella is accessible on foot, particularly if your hotel is near the Old Town or downtown areas. To travel further afield, a regular bus service runs to Puerto Banús and beyond. Taxis are abundant and can offer a quick journey to another area of the town. For those after a slower pace of travel, there is a land train that runs along the promenade.
The national bus network in Spain is excellent and you can get coaches to many destinations from Marbella. To travel by train, head to nearby Fuengirola where you can get connections to Malaga to join the RENFE national rail network, with Cordoba, Sevilla, Madrid and Barcelona just some of the places you can go. Car hire is also a great way to travel around Spain, and if you're prepared to pay tolls the roads can be fast and almost traffic-free.