Iberia provides daily flights to and from Madrid and Barcelona from the airport situated nearby, half an hour from the city. There are also budget flights to and from London Stanstead and Liverpool airports by Ryan Air and from Gatwick by Monarch.
Connection to the city centre can be either by taxi (about 20€) or by a bus (3€). The bus takes about half an hour to reach its final destination, which is Palacio de Congresos. It leaves roughly on the hour but will generally be synched to a plane arrival. It has about 5 stops throughout Granada city centre including Gran Via de Colon (opposite the cathedral) and Triunfo. You can catch it back from stop 1a on Gran Via de Colon (next to stop 1).
Regular buses run from Seville and Malaga as well as some to Cordoba and a few direct services to the port of Algeciras. Malaga is well serviced by busses and is a good place to transt by if a direct serice is not available. The modern and organized bus station is located about 2 miles from the centre. It takes 13 minutes by bus (Bus 3 and 33, outside the Cathedral on Gran Via de Colon) to reach the city center, or reasonably cheap taxis are also available.
Three trains run each day on the picturesque line to Algeciras (gateway to Morocco) via pretty Ronda. Trains also run to Cordoba, Malaga and Almeria. More information and ticket sales at the national railways webpage.
The town is small enough to walk around, although the Arab Quarter is on a hill. A quarter of an hour Hourly Minibus up the other hill to the Alhambra for the lazy/old. If you are not staying downtown and are going to make frequent trips to the city center, the best deal is buying a 21-journey ticket on any bus for about 10€.
If you intend to stay in Granada any more than three or four days the Bono card is a good investment . Valid for a week, it provides entry to the Cathedral, Capilla Real, Alhambra & Generalife, Monastery of La Cartuja, Monastery of San Jerónimo, Parque de las Ciencias (Science Park) and provides a 25% discount for non-EU citizens who visit the Fine Arts and Archaeological Museum. It also gives 9 urban bus journeys (to the bus station, science park etc.) and a 24 hour ticket to the tourist bus. Cost is €34.
It is highly recommended to book tickets to the Alhambra as it is usually booked out at least a few days in advance. These can be purchased Online of if you're already in Spain at branches of the BBVA bank. Serveral hundred tickets are reserved for sale on the day but these usually require arriving early and queuing for an hour or two. The Bono card can be still available after the regular tickets have sold out. Failing that, quite a lot of the site is accessible without a ticket.
Many restaurants and bars are located outside on the plaza at the end of the 'chino' walk with a view of the Alhambra. Granada is notable as most of it millions of bars will serve free tapas with each drink. If you want to try a local wine ask for "un costa" – the quality is extremely variable and it is more like sherry (but not fortified) than a table wine.
The best deal might be the Youth Hostel , situated inside the Albaycín, close to the action. Maps to it can be found in the NevegaWeb internet cafe.