Read on for quick answers to "How can I get there?"
There are three airports:
Cheap flight and carrier airlines fly direct to Edinburgh from many destinations (list here). Glasgow is at least as well served.
Edinburgh and Glasgow also connect well to major hubs. London will usually be the easiest hub.
Many foreign hubs connect directly to Edinburgh, including Amsterdam, New York and Toronto.
The bus from the terminal costs £6 return (less online and £2.20 return if you walk to the park&ride on the airport boundary). After 25 minutes, arrive at Princes Street / Waverley station and get one of the many buses or walk half a mile south to Infomatics. A taxi from the airport will cost ~ £20 and take 20 minutes. More details here.
Get the bus into the centre (every 10 - 15 minutes, taking ~ 20 minutes, costing ~ £5 return). Catch one of the frequent ~ 45 minute trains to Edinburgh Waverley, costing ~ £10. Then as above.
Prestwick station is next to the airport. Rail tickets from Prestwick (already cheap) are half price if you arrived on a Ryanair flight - just show your boarding card to get the discount. (This applies to a return ticket to any destination, so if you are coming early for a holiday further north in Scotland, it can be useful.) Frequent trains reach Glasgow in 50 minutes. Change to the Edinburgh train, then as above.
Ferry: the overnight ferry from Amsterdam to Newcastle is a pleasant way to get you and your car to the north of England while you sleep. For a large car, two people and a cabin with a porthole, this was £360 return when I last did it. Allow 2.5 hours for the coastal drive from Newcastle to Edinburgh, longer for the scenic (and in miles shorter) route through the border towns. Book reasonably well ahead to be sure of your place (and, possibly, as with flights, to save money).
Train from Europe: the Eurostar service by train through the channel tunnel takes just over 7 hours to reach Edinburgh from Paris (less than 7 hours from Lille). Bahn.de has a good interface and many languages to check connections.
Flying: Edinburgh has good cheap-flight connections to almost every airport in the UK, as does Glasgow. Typically, flights take at least an hour but much less than two. Easyjet is one likely cheap flight airline for Edinburgh and Glasgow International, Ryanair for Edinburgh and Glasgow Prestwick, and Flybe can be worth checking. Among carriers, I have known BA to be cost-effective at times. Look at the airport web pages (e.g. flight arrivals) to find others.
Trains take ~ 4.5 hours (daytime - there are also overnight sleeper trains) to reach Edinburgh's Waverley station from London's King's Cross / St Pancreas station. King's Cross is at least 45 minutes from Stansted and much longer from Heathrow or Gatwick, so flying to London and taking the train will be slower than flying to London and then flying onwards. Whether it is costlier than flying depends on whether you are booking early (when flights are cheap) or late, and whether you are lucky enough to find a rail special offer.
Car: it will take you 7 hours to drive to Edinburgh from London, 6.5 hours from Bristol, 5 hours from Birmingham and 4 hours from Manchester. (Driving overnight reduces these times.)