There are direct flights to Edinburgh and Glasgow from across the UK and Europe, though from London it’s much easier to take a train. See National Rail for details and tickets.
If you’re saving pennies, getting a bus is cheaper, though the journey takes much longer – London to Edinburgh can take over 9 hours but can cost as little as £14 – take a look at megabus for cheap tickets.
It’s easy exploring Edinburgh on foot or using local buses, while train links are good between the major cities in Scotland.
For more sightseeing and getting off the beaten track, a hire car is a good option. All the major hire car companies have offices around the country. Tours can also be a good way of covering a lot of territory and major sights in a short amount of time, without costing you the earth.