Getting to the capital of Scotland is very easy; There is a wide variety of flights that arrive directly from Europe to Edinburgh International Airport. To get to the city center (Weverley Bridge) you can use the bus service, which you find at the same airport, they leave every 10 minutes, the journey takes 25 minutes, and each ticket costs five pounds sterling. You can find them from 06:50 in the morning until 00:20 from Monday to Saturday, while Sundays work from 09:25 to 00:20.
Another alternative is to take a cab, which are located on the east side of the terminal, the journey is 20 minutes and the price is around 18 pounds.
If you want to rent a car you can do it at the same airport, look for the companies that offer the service. In this case you will have the freedom to visit up to the Highlands. But remember that in the UK you drive to the left.
If your flight arrives at Glasgow airport, you must travel 130 km to Edinburgh, you can take a train, which will arrive in 45 minutes, or a bus that takes 1 hour.