The Arlanda Express is the quickest, easiest and most environmentally smart way to get from Arlanda International Airport to central Stockholm. The trip only takes 20 minutes and there are two stops at the airport... one (South) under terminals 3 & 4 and one (North) under terminal 5. The train takes you to the Central Train Station located in downtown Stockholm. From there it is easy to get to any hotel in central Stockholm, whether by walking, subway or taxi. The present cost for the trip is 240 SEK for adults, 120 SEK if you are over 65 and up to 4 children (0-17yrs) may accompany a full paying adult for free. They do offer a special deal on weekends, holidays and the summer where 2 adults can travel for 280 SEK. Another tip... make sure you buy your ticket at the booth or in one of their ticket machines before boarding(all major credit cards accepted). Buying tickets on board costs 50 SEK extra!
While it is quick and easy, some people find it a bit expensive. There are buses that travel the same route and tickets cost 119 SEK for adults and the trip takes approximately 45 minutes. If you are several adults travelling together then a taxi is also more economical. The main taxi companies have fixed rates to central Stockholm around 520 SEK. Make sure you ask what their fixed rate is before getting in the taxi!