There are direct air services from London and other European cities to Edinburgh, Glasgow, Dundee, Aberdeen, Inverness or Kirkwall, and from North America to Glasgow or Edinburgh. All UK domestic flights and those from Scotland to places in the EU attract a US$15 departure tax and to other destinations it's US$30; a cost that's usually factored into the ticket price. From Europe it's often cheaper to fly to London then catch a train or bus north. It's a one-hour flight from London to Edinburgh, but once you add on the trip to and from the airport you're getting close to the four-hour rail trip.
Long-distance buses are usually the cheapest method of getting to Scotland, with a range of private operators undercutting the state operator. The budget Slow Coach which runs between Youth Hostels all over Britain goes as far as Edinburgh. A train from London can get you to Edinburgh in four hours, Glasgow in five, but tickets are fairly pricey. Scotland has ferry links to Larne, near Belfast, and to Belfast itself. In summer there is also a weekly ferry between Aberdeen, the Shetlands and Norway, and a twice-weekly ferry from Aberdeen to the Faroes.
For those with their own transport, main roads are busy and quick - Edinburgh is 600km (373mi) from London and it will take you about eight hours to drive it.