Stockholm has four airports that are connected to downtown Stockholm by airport coaches as well municipal alternatives.

The main internaional airport is Stockholm Arlanda Airport (ARN) is located 40 kilometeters (25 miles) north of Stockholm city. This airport offers a high speed train service called Arlanda Express to and from Stockholm's Central station.  Tickets are 280 SEK one way for adults 26+, Student discounts available. There are also airport coach buses, Flygbussarna which departs every 10-15 minutes between Arlanda Airport and the City Terminal (right next to the Central station). This is 99 SEK one way. Most afforadable is the FlixBus which connects from Arlanda Airport to City Center of Stockholm in 40 minutes (right by Central Station) with prices ranging around 50 SEK one way.

Other airports are Bromma Stockholm Airport (BMA)("city airport"),  Stockholm Skavsta Airport (NYO)( 100 km or 60 miles south of Stockholm) and Vasteras Airport (VST)(100 km or 60 miles west of Stockholm)

 

For more information about to and from all the airports go here.

Best way to get around Stockholm is by the Stockholm Public Transport, SL which is responsible for buses, underground trains, commuter trains and more in Greater Stockholm.

Recommendation- buy a SL card which cost 20 SEK and can be purchased at SL Centers, underground ticket booths, newsagent kiosks and at the airport. These can be charged with any sum and validated electronically. Each validation ("ticket") costs 31 SEK and lasts for 75 minutes. Buying single tickets without a SL Access card costs 44 SEK, and is generally more complicated. It'a also possible to buy a 7 day unlimited travel with SL card for 325 SEK. Cash is not accepted to board buses.