Russia, Kemerovskaya oblast, Tashtagolskiy rayon, poselok Sheregesh
It is not recommended to go by car all the way from Moscow. The road is about 6000 km with not much of infrustracture along the way.
Aeroflot Airlines, Siberia Airlines and Transaero Airlines are the local airlines which you can use to get in to the region. You can fly from Moscow Domodedovo or Moscow Sheremetyevo to Novokuznetsk (preferably) or Novosibirsk. A return flight costs $250-$400 with taxes and takes about 4 hours. Novokuznetsk is the closeset city to Sheregesh but there is only one daily flight by Siberia. It is hard to get tickets during the high season.
This place is too far from Moscow to take a bus from there. However, if you find yourself in Novokuznetsk or Novosibirsk you can take a local bus. from Novokuznetsk - 200 R ($7) one way, 3 hours journey from Novosibirsk - 300 R ($11) one way, 6-8 hours journey (depends on the route). There are more frequent buses to Tashtagol the town just in 17 km from Sheregesh. You can go to Tashtagol first, and then take a local bus form Tashtagol to Sheregesh or take a taxi for 200 R.
Direct train from Moscow to Novokuznetsk (about 60 hours, costs 1800 R ($70) one way). Direct train from Moscow to Novosibirsk (48 hours and costs 1200 R or $40 one way).