Aeroflot has been broken up into many small airlines, leading to virtually unregulated skies and the worst regional safety record in the world. Flying within Russia is an unreliable, unpredictable and difficult business. Try to get a seat on a domestic flight that ultimately has an international destination, because these carriers are certified to meet higher standards than domestic-only services.
European Russia is crisscrossed by an extensive rail network that makes trains a viable means of getting to practically anywhere. They're cheap and comfortable and usually take a long, long time. The rail network runs on Moscow time; the only general exception is suburban train services, which stick to local time.
Russian buses are now completely open to foreigners and when going between small towns are a great way to travel. Driving in Russia isn't everybody's cup of tea but, if you've got a sense of humour, don't mind some fairly rugged road conditions, a few hassles finding petrol, and getting lost now and then, it's a great way to see the country.
River transport remains important and in summer it's possible to travel long distances across Russia on passenger boats. The main passenger services ply between Moscow and St Petersburg, and between Moscow and various points on the Volga and Don, including Yaroslavl, Nizhny Novgorod, Volgograd, Astrakhan and Rostov-on-Don.