By train
Oslo Central Station Oslo Sentralstasjon/Oslo S, T-bane Jernbanetorget is at the eastern fringe of the city centre, by the end of the main pedestrian street Karl Johans gate. Oslo S is at the centre of Norway's railway, all lines including the airport express train terminate at Oslo S, making Oslo S the supreme gateway to Oslo. The major express buses go to the bus station next door to the train station.
Internationally, there are three daily services to Gothenburg Sweden 4 hours. Four daily trains travel in the direction of Stockholm Sweden 6 hours, two of which will require a change in Karlstad schedule (http://www.resplus.se/fetchpdf.asp?tt_id=625). The night train on this route is sadly terminated as of January 2009. For Copenhagen Denmark and beyond, but you will have to change trains in Gothenburg. However, in summer a limited night train network to Malmö and Stockholm is run by Swedish train company SJ.
Tickets for the Gothenburg line are cheapest when bought at the NSB (http://www.nsb.no) website, where the Minipris-fares run as low as 199 NOK. Tickets for the Stockholm line are cheaper if you buy them from the Swedish train company SJ's website (http://www.sj.se), where the cheapest tickets can end up as cheap as 95 SEK. Tickets are released for sale 3 months ahead of departure, and the sooner you buy them, the cheaper they will be. Both Norwegian and Swedish prebooked train tickets can be picked up at ticket machines in Oslo Central Station Norwegian tickets also at other stations.
Norwegian state rail operator NSB (http://www.nsb.no/) run fairly frequent and half-efficient, though not very fast, domestic services to Stavanger, Kristiansand, Bergen and Trondheim, as well as a relatively comprehensive, but flaw-marred, local and regional service around Oslo. Their schedules are here: (http://www.nsb.no/rutetider/).
Long-distance trains heading south- or westwards also stop at Lysaker station at the western city border. Those heading north and east make their first call at Lillestrøm station, outside of the city.
For people using Oslo as a point of transit, it is good to note that the building just south of the main central station is still part of the train station and has lockers for rent. The small lockers are 30NOK, the medium lockers are 40NOK and the large lockers are 60NOK. The medium lockers also come in two shapes, cubic and thinner but taller, make them useful for storing luggage which would not normally fit.
By ship
Oslo is connected to Denmark and Germany by car ferry. Color Line (http://www.colorline.com/) runs services to Kiel Germany daily. DFDS (http://www.dfds.no) runs daily services to Copenhagen Denmark, and Stena Line (http://www.stenaline.no/) provides service to Frederikshavn Denmark.
You may also want to consider Color Lines high-speed boats from Larvik 2 hours south of Oslo on E18, or easily reachable by hourly NSB train or Kristiansand 4 1/2 hours south of Oslo on E18, or reachable on five daily trains or near-hourly buses to Hirtshals Denmark. They both take some 3 1/2 hours to reach Denmark.
The port for cruise lines is near Akershus Festning, a short walk from downtown. The train station in Kristiansand is close to the ferry quay, while in Larvik the quay has been moved to a location which is a bit of a trek from the station.
By car
International highways E6 from Malmö and Gothenburg and E18 from Saint Petersburg, Helsinki and Stockholm meet in Oslo. There is a road tax of NOK 25 to enter Oslo with a car. The money is used for road construction and public transport. The toll booths are non-stop, and will snap a photo of your license plate and send the bill to the car owners' house. In addition, when entering the city from the west, an additional tax of NOK 12,50 is charged on the municipal border at Lysaker to finance the construction of a new highway leading westwards.
The E6 is the main north-south road of Norway, and continues north to Trondheim, Alta and Kirkenes, with branches to most Norwegian cities. The E16 runs west to Bergen, the E134 to Haugesund and the E18 run south-west to Drammen, Grenland Skien/Porsgrunn and Kristiansand. Other notable roads into Oslo include Rv4 from Gjøvik, Rv2 from Charlottenberg Sweden and Kongsvinger and Rv7, an alternative road to Bergen passing Gol and Geilo..