Oslo has several airports, each about an hour from the city. The closest and largest is Oslo Airport Gardermoen, and from there the express train takes approximately 20 minutes to Oslo Central Station and costs about US$30. Local trains and airport buses will also take you around Oslo and the outskirts.
Though not a highly populated city, Oslo covers a lot of ground. The city is walkable but also offers the standard transportation options (metro, tram, bus) as well as bike rentals—Oslo's version of London's Boris Bikes. You can use the same ticket on all public transit within the city, and a standard 24-hour ticket costs just under US$14. There are also taxis aplenty, but be warned—they are expensive.