No visa is required for visitors from Abkhazia, Armenia, Azerbaijan, Belarus, Bhutan, Bolivia, Botswana, Bosnia and Herzegovina, Brazil, Brunei, Cape Verde, Chile, Colombia, Costa Rica, Cuba, Dominica, Dominican Republic, Ecuador, El Salvador, Fiji, Grenada, Guyana, Honduras, Hong Kong, Israel, Jamaica, Kazakhstan, Kyrgyzstan, Laos, Macau, Maldives, Mauritius, Moldova, Mongolia, Montenegro, Namibia, Nauru, Nicaragua, Palau, Panama, Paraguay, Qatar, Saint Vincent and the Grandines, Saint Kitts and Nevis, Samoa, Seychelles, South Africa, South Korea, South Ossetia, Suriname, Tajikistan, Thailand, UAE, Ukraine, Uruguay, Uzbekistan, Vanuatu and Venezuela
Others will need a visa and probably 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 can be 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.
Transit visas can be arranged that are valid for 3 days. They may be a lot easier to arrange.
Russia visa requirements