There are daily flights to and from London, Luton and Manchester in the UK. There are no regular buses to Gibraltar, but the bus station in La Línea is only a five minute walk from the border. If you're driving, lines at the border may make it less time-consuming to park in La Línea and walk across. The land border is open 24 hours a day.
There is normally one ferry a week each way between Gibraltar and Tangier, taking two hours. The ferries accommodate cars.
The 1.5km (1mi) walk from border to town centre is quite fun as it crosses the airport runway. Alternatively, several bus lines run from the border into town. All of Gibraltar can be covered on foot, and much of it (including the upper Rock) by car or motorcycle. You can also ascend the rock by cable car.