First of all, you need a letter of invitation from a friend or relative in Russia. Ask the person you are visiting to go to a local Passport and Visa Service office of the Ministry of Internal Affairs of Russia and obtain the invitation letter.
Make a copy of your passport's pages with your name and signature on it. Make sure your passport has two blank pages for the visa.
US citizens must fill out the application form found here: http://www.consulrussia.org/docs/Visa/Form_USA_eng_letter.pdf
Non-US citizens must fill out the application form found here: http://www.consulrussia.org/docs/Visa/Form_NonUSA_eng_letter.pdf
Make a money order or a cashier's check for $250 if you want the processing to take 3 days and $131 if you do not mind if the processing time is between 4 and 20 days. Make payments payable to the Russian Consulate General.
You must also write a cover letter specifying the purpose of your visit, dates of arrival and departure, cities to be visited in Russia and the telephone or fax number where you can be reached.
If you fit into any category below, please visit the following website: http://www.consulrussia.org/eng/rules.html
Children
Guests of foreign diplomatic staff
EU citizens
Former USSR and Russian citizens
German citizens
Canadian citizens
Citizens of Estonia, Israel and Finland, as well as for the citizens of Schengen Agreement Member-States (Austria, Belgium, France, Germany, Greece, Italy, Luxembourg, Netherlands, Portugal, Spain and other Schengen states)
US citizen staying over 6 months
Non-US citizen staying over 3 months
Need a double-entry Visa