Stockholm has two main airports: Stockholm-Arlanda (ARN) and Bromma Stockholm Airport (BMA). Both service international flights. Stockholm-Arlanda is the major one
and services flights from all over the world, whereas Bromma Stockholm is more limited
but closer to the city center.

For transfer Stockholm-Arlanda we recommend Arlanda Express (20 minutes, train, one way ticket is 260 SEK ≈ 28 €) or Flygbussarna (45 minutes, bus, one way ticket is 119 SEK ≈ 13 €). For transfer from Bromma we recommend Flygbussarna (20 minutes, bus, one way ticket is 74 SEK ≈ 8 €).

Stockholm is full of more or less serious taxi companies. Be careful, you can be completely ripped off if you get into the wrong taxi!
We recommend Taxi Stockholm (+46 8 150 000), Taxi Kurir (+46 8 300 000) or Taxi 020 (+46 20 20 20 20). They always have cars at both airports and in the city.

There is a third airport in the Stockholm area, Skavsta (NYO). It serves low fare airlines (Wizz, Ryan Air and more). From Skavsta we recommend Flygbussarna (75 minutes, bus, one way ticket is 129 SEK ≈ 14 €).