By taxi
Official airport taxis currently cost around $60, or if you prefer you can book an airport transfer to meet your flight here. The drive to the Sayany Hotel should take around 40 minutes.
By train
Aeroexpress trains run from Sheremetyevo Airport Station (behind Terminals D, E and F, with a free bus connection from Terminal B) to Belarus Rail Station in downtown Moscow. Trains run every 30 minutes from 5am to 12.30am daily, with a journey time of around 35 minutes. Standard adult tickets cost roughly $11. Then take the metro from Belorusskaya Metro Station and travel two stops clockwise on the brown circle line to Prospekt Mira. Change there to the orange line and travel north three stops to VDNKh Metro Station. The Sayany Hotel is around 15 minutes by bus from the metro.
By bus
There are also buses running from all terminals at the airport to Rechnoy Vokzal Metro Station. However, as you will then need to take the metro all the way into central Moscow and change lines twice before heading back to the far north of the city and then taking a bus to get to the hotel, this option is definitely not recommended.