As in every travel the most expensive is flight.
Inside the country it's not so expensive.
When i was in Moscow last time i found not bad hotel for about 30$ day.
But Moscow is the most expensive city in the country.
If u wonna visit other cities, u have to be ready for long trip and expensive tickets, cause this country is huge.
The most cheap way to travel in Russia is by train, but it takes much time.
f.e. if u wonna have travel from moscow or sankt-peterburg to Lake Baikal (with some cities to visit by the way) u must spend about 1.5 week just in the trip.
To travel by the airplanes in russia is much more more expansive than in europe.