Just follow the signs for the train, bus or taxi:
Train Arlanda express to STOCKHOLM-C
Price: 190 SEK
Duration: 20 min
Departure: every 15 min
The station is located right below the arrival hall of the airport. You will arrive at the central train station in Stockholm with direct access to the subway.
Bus Flygbussarna to CITYTERMINALEN
Price: 89 SEK (59 SEK with a student ID)
Duration: 35 min
Departure: every 10-20 min
Buy the ticket at the office in the arrival hall. The bus station is right outside the arrival hall. The bus has only few stops and CITYTERMINALEN is the final destination with direct access to train STOCKHOLM-C or subway T-CENTRALEN.
Taxi to any location in central Stockholm
Price: approx. 400 SEK (Ask for the flat rate!)
Duration: ca. 40 min (or more, depending on traffic)
Departure: The taxi stand is located just outside the arrival hall.
Ask for a flat rate to your destination in Stockholm before you board the taxi! It should will be around 350-400 depending on the company. If you are not satisfied, you may board not the first taxi in line. The fixed price is usually written on the car. Even so, if you do not ask for the fixed price, they may turn on the meter and charge you much more!