From Stockholm-Arlanda Airport:

The Arlanda Express high speed train runs between Stockholm city centre and Arlanda airport. The train leaves from terminals 2, 3, 4 and 5 and travels to Stockholm central station in 20 minutes. Adult tickets are SEK 200 and children under 17 accompanied by an adult travel for free.

Flygbussarna airport coaches depart regularly from terminals 2, 4 and 5 for Stockholm city centre. Travel time is 40 minutes and return tickets are SEK 175.

Taxis are available outside all of the airport terminals. Taxis offer a fixed price for journeys so be sure to agree a price before you depart.

Car hire is available through all the major car hire firms inside the main terminal at6 Arlanda airport.

Getting around Stockholm:

Public transport in Stockholm is vast as would be expected from a city of its size and importance. There is a good network of bus routes that connect the whole city and a metro system with three lines that must be witnessed to be believed (The metro system in Stockholm has been described as the largest exhibition in the world).
Stockholm also has a heritage tram line and light railway system.
All of the public transport in Stockholm is run by Storstockholms Lokaltrafik AB, commonly referred to as SL. Tickets for transport on the public transport system are sold as either single journey tickets, valid for up to one hour after purchase or travel cards valid from 24 hours to 1 year. Single tickets are SEK 20, 1 day travel cards are SEK 60, 3 day travel cards are SEK 180 and 7 day travel cards are SEK 220.

The Stockholm archipelago is served by seaborne public transport that is operated by the Waxholmsbolaget. The ferries serve the whole of Stockholm’s inner harbour area and SL travel tickets are valid for journeys on the ferries.