There are two airline companies flying to Khanty-Mansiysk from Moscow: transaero.ru and utair.ru. The flight lasts 2 hours long. Transaero is cheaper, the round flight costs 200-250 euro.
There is no railway station at Khanty-Mansiysk. But if you want to come by train you can buy a ticket to Surgut or Pyt-Yakh (Пыть-Ях) and then take a bus (3-4 hours). The Russian railway’s webpage is rzd.ru. Round tickets for the third class (so called platzkart) would cost 180-200 euro, and the trip would last 40-45 hours long (good for funs of the Trans-Siberian trip).