Stockholm has an extensive system of buses but we didn’t use them much because we found the T-bana or walking was better for most areas we wanted to go to. The exception was the route from the Stallmastaregarden Hotel to the central city. Buses can be slow when caught in traffic in the central area but you can also get around fast elsewhere, because they can use special bus tracks on many roads.
The city's transit system has several types of buses. These include Red buses which cover routes within the central city, Blue buses which connect the city center and major Tunnelbana stations with outlying areas, and in the early hours of the morning when the T-Bana or subway isn't running, Night buses fill in for the sleeping trains.
You can buy bus tickets on board, at any transit station, or at Preebyran newsstands. A single-ride ticket is good for two hours of travel with unlimited transfers. Alternatively, you can use 10- or 20-ride ticket books, unlimited travel passes, or the Stockholm Card for travel. We used this card and found it incredibly useful.
The easiest way to see the city of Stockholm is by taking the blue buses, no 1, 2, 3 or 4. They cover most of the city centre and you can use your Stockholm Card on all the buses. A comprehensive Stockholm guide showing all the points of interest other than museums etc. is not included, but you can always ask one of the local passengers if you see something interesting and there is a good chance they can help with information. During peak hours the buses run about every five minutes so if one comes that is too crowded you just wait for the next one.
Number 1 runs from Stora Essingen to Frihamnen and covers Kungsholmen through the City and Östermalm. Number 2 runs from Sofia on Södermalm to Norrtull via Norrmalm and Vasastan. Number 3 takes you from Södersjukhuset to Karolinska Sjukhuset via Kungsholmen. Number 4 will take you on a trip from Gullmarsplan to Radiohuset and show you parts of Södermalm, Kungsholmen and Vasastan.
If you want a more formal tour I suggest you make a tour with one of the open-top double-decker buses. You will see all of the city's main sights and guiding is provided in several languages through individual headphones. If you buy a Hop-On Hop-Off ticket you can get off at various points to explore the area, and get back on the next bus later - without having to pay extra.