To apply for a russian visa you need:

a "tourist invitation". The invitation consists of two documents: the "confirmation" and the "voucher" 
you can get it here: "apply now")
an application form with a passport sized photo ( get the form here: "download application form")
your original passport with at least two blank visa-designated pages (passport must be valid for at least 6 months after intended departure date from Russia)
a document that proves, that you have a valid health insurance for Russia. (Not all consulates require this but most consulates in Europe do. You can buy an additional travel health insurance at a travel agency.)

Costs of invitation letters:

We offer the following tourist invitations:
3 days, single entry: 15
2 weeks, single entry: 29
4 weeks, single entry: 47
2 weeks, double entry: 49
4 weeks, double entry: 75

If you have an official invitation you can:

apply for the visa yourself at your local Russian Embassy/Consulate
or: engage a visa agency to apply for the visa on your behalf

Consulate Regulations:

Some consulates have their own regulations or are stricter in obeying Russian visa rules. If you want to be on the safe side contact your nearest embassy/consulate. Here are the main consulate rules:

Visa processing starts only after you have delivered all necessary documents. All paperwork once submitted is not subject to any change.
The fee for visa processing is not refundable. In case the applicant requests correction of the visa due to various reasons (except mistakes of the consulate staff) the applicant will have to re-apply for a new visa.
The consulates have different processing periods. Normally the slowest though cheapest period lasts about 3 weeks whereas the fastest way would cost you more than 100 Euro.
Tourist visas must be issued al least 2 days prior to departure stated on the invitation.
the visa will be issued exactly as indicated on the invitation. You can travel to Russia within the visa period.
Please note, that Russian consulates are closed during Russian holidays (sometimes also the day after) and on holidays of the host country.

Required documents and further information: