DOCUMENTS NEEDED. If you have a passport, which expires at least three months after your visa expires, 4 standard passport photos, then all you need is an invitation from Russia. Also, maybe you'll need an insurance - depends - and of course you need some money for visa processing ($43 - $75 US).
After you have all the documents, you need to fill in the visa application form. You can see a sample of the visa application form that is given in th Russian consulate in USA here (in adobe acrobat format).
Requirements of Russian consulates vary from country to country, so you should check with the consulate you will apply to, what documents you need (see our Russian Consulates Worldwide page for the contacts)
WHAT IS AN INVITATION. The invitation is easy to get, and you don't have to book a hotel / hostel for the whole period of your stay to get it. There are different kinds of invitations, depending on the type of visa you need:
TOURIST INVITATION. You need a tourist invitation if you plan to stay in Russia up to one month. The tourist invitation can be issued for a single- and double-entry Russian visa. If you need a multi-entry visa or you plan to stay more than one month, then you need an invitation for a business visa.
A tourist invitation is a special voucher, a reservation confirmation, and a letter from the inviting party (a travel agency or a hotel / hostel), all the papers together (called "invitation") cost from $25 US to $50 US, depending in the company you choose.
The tourist invitation can be faxed or posted to the Russian consulate (depends if they accept copies and faxes or not).
The invitation are the papers from the inviting part (a travel agency or a hotel / hostel) addressed to consulate department of Russian Federation in the country you're in. These papers are signed and stamped by the inviting organisation. The inviting party must have a "reference number in the Ministry of Foreign Affairs" and the "number of license" and they must print them on the invitation papers.
The voucher is a paper with your name and passport details and the inviting part's name, reference number, license number and contact data on it. There's also the dates of your visa on this paper.
The reservation confirmation is a confirmation that you'll live somewhere. There's also the dates of your visa.
You must come and leave anytime during the time span of your visa.
In almost every country russian embassy "prefers" originals of those papers (that is they accept faxes, but prefer it directly from the inviting party, or better - by post), in some countries or cities they only accept originals, and this rule depends only on the person who will be accepting your documents.
TRANSIT VISA. You don't need an invitation for a transit visa, but you need valid tickets to Russia and a visa to the country you'll go after Russia (if the visa is required).Generally transit visa will be cheaper than touristic, because to get touristic visa you need an invitation that costs around $25 US. But the price of transit visa processing is the same as for tourist visa.
BUSINESS INVITATION. If you want to stay in Russia more than 1 month or want a multi-entry visa, you need a business visa. The reason is that Russian consulates are reluctant to give tourist visas for the period more than 1 month, because they don't believe you're just a tourist for so long. Business visas are the same as touristic except that the invitation for business visa is made at MID (Ministry of Foreign Affairs), it takes a bit longer to make it than the tourist invitation.
The invitation for a business visa is just one paper from MID, that has all the data: your name, nationality, dates of your visa etc.
Also, business visa means some business invites you in Russia. It can either be the company you work in right now or some other company in Russia. Most business invitations to Russia are made by travel agencies, which make it seem as if they invite you for some business to Russia. It's not illegal, and the business invitaiton is a good option if you want to stay longer than 1 month, or you're not sure when you want to enter Russia, and want to leave yourself a time span.
Note, that although to make a tourist invitation you just need to send to the agency you personal data, to apply for a business invitation you also need a copy of your passport's first page (the one with your photo and name) sent to the agency.