Åndalsnes is the end station og the Rauma Railway (Raumabanen in Norwegian), which traffics the stretch between Åndalsnes and Dombås. At Dombås there is connecting trains to Oslo and Trondheim. There are 3-4 trains to and from Dombås each day, all of them connects to Oslo and Trondheim. If you book early you can get tickets for 199 norwegian kroner for any streach of railway in Norway (booking at www.nsb.no). The Rauma Railway is also considered to be one of the most beautiful railways there is, and during the summer they often have guides on board the train. From the train you can get a good view off the Trollwall and a lot of spectacular nature. So I recommend taking the train at least to or from Åndalsnes.
There is an express buss connection between Åndalsnes and Oslo with one trip in each direction during the day, and one overnight trip. This buss connection is called "Dag og Nattekspressen" and has route number 142, schedule and booking can be found here
There are also bus connections several times a day to Molde and Ålesund, both of them have an airport, and Hurtigruten dockes in these cities .
Norway Bussekspress operates a bus connection that departs at 10 AM(day bus) and 10 PM(overnight bus) from Oslo to Åndalsnes.
The bus also connects to/from Molde and Ålesund
Link to english version in the top left corner of the page.
If you arrive to Åndalsnes from the north you can take the ferry between Sølsnes and Åfarnes. It saves you a long drive around.
The ferry takes about 10 minutes, and departs many times per hour.
North of Åndalsnes lies places like Molde, Bud, the Atlantic Road and Kristiansund. All of them worth a visit!