The main airports are in Montego Bay and Kingston, and both of these have direct flights from the UK every day, courtesy of British Airways and Air Jamaica, but you can also fly via the USA easily.
Small internal services operate between the main airports, and the smaller resort towns of Negril, Ocho Rios and Port Antonio. There is a comprehensive, but unreliable bus network that operates without the need for timetables, but does connect practically everywhere with everywhere else.
Hiring a car is an excellent way to see more of the island, but the roads are not always of the highest standard, and some of the driving that you might encounter leaves a little to be desired. Make sure you have adequate insurance and a great deal of patience. Jamaicans almost always drive on the left, except when they don't.