It on the Kola road (M18) from St. Petersburg to Norway. Highway A132 to Norway and P12 to Finland begin in Murmansk. As of Summer 2013 the highway is in very good shape, by Russian standards.
The Murmansk airport is actually in Murmashi, 24km south-west from Murmansk. Daily flights to Moscow and St. Petersburg. Regular flights to Arkhangelsk, Tromso (Norway), Helsinki (Finland), Turkey, and Egypt.
3-4 direct Moscow to Murmansk trains, and several more from the South of Russia passing through Moscow on their way to Murmansk.
Avoid southern trains! Unless you enjoy noise and bo. Hop on one originating in Moscow or St. Petersburg if you have a choice.
Total time in transit is about 40 hours. Second class tickets from Moscow to Murmansk from $80 to $170 as of April and May of 2013.
I’m giving $US equivalent because some think that yet another rouble collapse in imminent and prices quoted in Roubles may not soon have much meaning.
Most Moscow to Murmansk trains go though St. Petersburg but some via Volkhovstroy. If you have a choice and don’t need St. Petersburg take a train that goes through Volkhvostroy. These are much less crowded, and in the winter downright empty.
Feel fee to ask for advice. Alexandra has been travelling the Moscow to Kandalaksha route (just 300km short of Murmansk) for thirty years and is regularly asked how to get from Moscow or St. Petersburg to here with minimal strength and expense.
But if, as most foreigners, you are set on this awful Trans-Siberian concept, Olesya is the best Trans-Siberian expert I can recommend. Originally from Tomsk, now based in Moscow, and in a good position to help travellers with advice (free) or making specific arrangements (for a very reasonable fee). Contact details on Olesya’s site >>