You need a visa to travel to Russia. If you are traveling with a travel agency or a tour, they will take care of this for you.
Now there are many other ways to get a visa. Basically you need an "invitation" either from your host or some sort of host organization, institute, or official agency, stating that they will take all responsibility for your needs. A foreign-owned company must be registered with MID to issue such an invitation. You then send the invitation to the Russian Embassy along with three photos, a visa application, photocopy of your passport, processing fee, and stamped return envelope. Some organizations, for example the new Bed & Breakfast Associations, will get a visa for you. There are also visa services that will help you get the "invitation" that is necessary for a visa if you are not traveling with a tour.
The Russian Embassy in Washington and the Consulates in New York and San Francisco now have accelerated processing:
Single-Entry Visa: two weeks processing time is $70, one week $80, three business days $110, next business day $150, same business day $300.
Double Entry Visa: two weeks processing time is $120, one week $130, three business days $160, next business day $200, same business day $350.
Multiple Re-Entry Visa: three business days processing time $200, next business day $350, same business day $450.
The New York office is particularly efficient. Prices may change.