On the territory of Altai Region there are 2 airports: Barnaul (BAX) and Gorno-Altaysk (RGK).
Both airports have flights from Moscow.
Barnaul takes flights from St. Petersburg, Tomsk and Krasnoyarsk.
Gorno-Altaysk has flights from Krasnoyarsk and Novosibirsk.
The railroad exists only till Barnaul and Biysk. From Moscow you can go to Barnaul (via Ekaterinburg and Omsk). Barnaul is connected also with Novosibirsk and Krasnoyarsk. From Barnaul to Biysk you can travel by shuttle trains. There is a passenger train from Novosibirsk to Biysk.
All further transportation around Altai region is possible only by high way roads (public buses, touristic transfers).