Edinburgh Airport, 7 miles west of the city center, offers only a few transatlantic flights. It does, however, have air connections throughout the United Kingdom -- London (Heathrow, Gatwick, Stansted, Luton, and City), Birmingham, Bristol, East Midlands, Humberside, Jersey, Kirkwall (Orkney), Inverness, Leeds-Bradford, Manchester, Norwich, Sumburgh (Shetlands), Southampton, Wick, and Belfast (in Northern Ireland) -- as well as with a number of European cities, including Amsterdam, Brussels, Copenhagen, Cork, Dublin, Frankfurt, Paris, and Zurich. Flights take off for Edinburgh Airport virtually every hour from London's Gatwick and Heathrow airports; it's usually faster and less complicated to fly through Gatwick, which has excellent rail service from London's Victoria Station.
There are no rail links to the city center, despite the fact that the airport sits between two main lines. By bus or car you can usually make it to Edinburgh in a comfortable half hour, unless you hit the morning (7:30 to 9) or evening (4 to 6) rush hours. Lothian Buses run between Edinburgh Airport and the city center every 15 minutes daily from 9 to 5 and less frequently (roughly every hour) during off-peak hours. The trip takes about 30 minutes, or about 45 minutes during rush hour. A single-fare ticket costs £3.
You can arrange for a chauffeur-driven limousine to meet your flight at Edinburgh Airport through David Grieve Chauffeur Drive for about £45 plus V.A.T; Little's Chauffeur Drive, £47 plus V.A.T; and W L Sleigh Ltd., £50 plus V.A.T.
Taxis are readily available outside the terminal. The trip takes 20-30 minutes to the city center, 15 minutes longer during rush hour. The fare is roughly £20. Note that airport taxis picking up fares from the terminal are any color, not the typical black cabs.