These are the best way to travel, but again there is a dual price system. All foreigners must purchase their tickets from Intourist at extremely inflated prices. There will be an Intourist ticket booth at all train stations in Moscow and Saint Petersburg. You can travel at Russian ticket prices if you get your ticket purchased by a Russian for you, but you run the risk of being caught, and most likely you will be. If you are traveling with a Russian, it is then possible to get away with this. And if you do get caught later on the train, you will just have to pay a bribe to the Conductor $10-15 US no more. You should also lock your door in your train compartment at all times and when sleeping at night secure it with a belt. Never leave your baggage unattended. Tourists are targets on trains, as they are perceived to have lots of money. Police do patrol the train on board, but we know how much help they will be.
They are now enforcing Visa requirements for traveling to other cities. Technically you can not travel to other cities then what are listed in your Travel Visa. If your documents are checked when trying to get on the train, you will most likely be refused entry to the train. If your documents (Visa) is checked in a city other than what is in your Visa, you can be arrested, but most likely you will be asked to pay some money.
WARNING: DO NOT TAKE PHOTOS AT THE TRAIN STATION! THEY SEEM TO HAVE A PROBLEM WITH THIS TOO.
There are several classes of trains from the very fancy to the old and plain. You can travel in a Cabin for two (recommended), Cabin for four or an open car (appox 50). Train food is very bad, purchase your own and take it on the train with you. Russians never buy food on the train. Also bring your own supply or toilet paper, as I can guarantee there won't be any.
Note: Many trains are being cancelled due to lack of use, so be prepared. There is also electric trains that are cheap (two hour electric train ride to Tanarog from Rostov-on-Don cost me .50 cents!) And run very often between cities, and villages. They are located usually next to the Train Station and Bus Stations. They are not in great condition but are fun to travel on for day trips. They have wooden benches inside, vendors will come through selling ice-cream, magazines, beer, etc. There will be panhandlers playing music, and beggars looking for money. They now have electronic tickets dispensers at the electric train stations, but unless you understand Russian best to buy your tickets at the ticket window, you will have better luck, tickets can be used on any train that day, they can also be bought in advance.