hi there,
The cheapest and most convenient way to get around Russia between cities is by bus as buses have more regular departures than trains. Most bus journeys between
cities cost less $20.
With trains you must book tickets in advance and you need to present your
passport or you wont be able to buy the tickets. You have two types of trains, slow and fast ones. The fast ones cost around $50 for the same journey as a bus so, you can see the difference here.
Also, reserve tickets at least 24 hours in advance and be aware that queues can be very long so prepare yourself.