You need a visa if your not from the CIS, Argentina, Bosnia, Brazil, Chile, Colombia, Cuba, Ecuador, Fiji, Hong Kong, Israel, Macau, Macedonia, Montenegro, Nicaragua, Peru, Serbia, Thailand, Turkey, Uruguay and Venezuela. Others will need a visa and an invitation.
You will need to pay for the invitation, then pay the consulate and you will need to register when you arrive. Regulations are very painful, do not expect to travel very far without some sort of support. The visa regulations for Russia are costly, tedious and take a lot of time.
You may also need to supply proof of medical insurance, copies of bank statements, a letter from you employer and more.
If you wish to travel for longer than 30 days you may need establish some "contacts" who can help you arrange a business or special visa.
Transit visas can be arranged that are valid for 3 days. They may be a lot easier to arrange.
Embassy of the Russian Federation, main page
List of Russian visa charges and details