Taxi: There are always taxis available outside the terminals. A ride to the city center is about 500 SEK (approximately 50 EUR). The ride takes 30-60 minutes depending on the amount of traffic.
Flygbussarna (airport coaches). Has several routes depending on what part of Stockholm you’re going to. A single ticket from Arlanda to Stockholm city is 99 SEK (approximately 10 EUR). The ride takes 50-60 minutes.
Flixbus. Pretty much the same as Flygbussarna but cheaper. Tickets start at 39 SEK.
Public transport in Stockholm (1): You can take a bus to Märsta, followed by a regular commuter train to Stockholm City. Note that if you buy e.g. a 72-hour ticket for unlimited travel in Stockholm, going to Stockholm City this way is included. It also takes the longest time, 75 – 90 minutes depending on the connections.
Public transport in Stockholm (2): You can pay to access the commuter trains immediately at Arlanda. This costs 150 SEK (approximately 15 EUR) for a single ticket including passage, and the ride takes 40 minutes.
Arlanda Express, a train departing up to six times per hour. An adult ticket is 280 SEK (approximately 28 EUR) and a youth ticket is 165 SEK. The ride takes 20 minutes.