From Arlanda airport
The largest airport in the Stockholm area is Arlanda. To get from Arlanda to Stockholm City there are four main alternatives: Taxi, Arlanda Express (fast train), Arlanda Airport buses, and commuter train (pendeltåg). More information can be found here: http://www.swedavia.se/arlanda
From Bromma Airport
Bromma airport is the “local airport” in Stockholm and is located northwest of town, not very far from KTH. Therefore, the preferred way of transportation is with a local cab, but more information about different alternatives can be found here: http://www.swedavia.com/bromma/
From Skavsta Airport
Skavsta airport is a relatively small airport situated approximately 100 km southwest of Stockholm. Information about different transportation alternatives can be found here: http://www.skavsta.se/en/airport/
Information about local transportation (buses and subway system, “tunnelbanan”)
How to travel on the subway/commuter trains?
Option 1: Buy an electronic card and load any number of single tickets (in swedish “Reskassa”) or passes (24 h, 48 h, 72 h, weekly passes). Electronic cards are 20 SEK to buy (debit or credit card only) at SL Center (T-Centralen station and other major stations like Slussen, Fridhemsplan, and Tekniska högskolan), as well as in convenience stores such as Pressbyrån inside the train stations (always check for the SL logo!).
Option 2: Download the app from SL and buy tickets in the app
Option 3: Buy a single ticket at a vending machine in the stations within Stockholm (debit or credit only, no cash).
Option 4: Buy tickets at the subway/commuter train booth (more expensive than Option 1, and please note that only cash is accepted in the subway booths)
How to plan your journey (enter either a station or an address): Stocholm Länstrafik webpage