You should apply for visas as soon as possible. It may take some time so please apply ASAP just to make sure you get it far in advance.

The following documents should be submitted to the Russian Embassy or Consulate to obtain a Tourist Visa to enter Russia:
1. Your original passport with at least 2 blank visa-designated pages (passport must be valid for at least 6 months after intended departure date from Russia).
2. One of two copies of Russian visa application form, completed and signed (possible to fill online yourself: Visa Application – please, read instructions first or see this step-by-step guide).

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3. Two passport-size photos signed on the back (3.5×4.5cm which was taken no longer than 6 months prior to the application submission).
4. Travel insurance if you don’t have it.
5. It is not necessary to have a hotel reservation in order to get a visa but you do need a visa support letter. A visa support letter is a confirmation of hotel arrangements from authorized Russian travel company, or directly from the Russian hotel, showing reference number and confirmation number for the visa.
Usually, a hotel issues such an invitation for free, but it is also possible to get such an invitation from a touristic company. It costs about 15-20 USD and can be obtained online at multiple websites.
For example: You can get a touristic visa support letter and insurance (can be added or not) here Visa Invitation or only an invitation here Quick Visa Invitation if you want it really fast (in 5 minutes).
You should print this PDF file IN COLOR (consulate can take black and white but better not to risk).
Note: There is a very small chance that you will be asked for an original of a visa support letter but in last few years we haven’t heard about such a request for a touristic visa. Please, call to your consulate to minimize the risk.

Note: From January 2015 visa applicants from the United Kingdom, Denmark, Myanmar and Namibia are obliged to provide fingerprint scans.

Consular Fees (information from the web):
Single-Entry, processing time 6 – 8 business days:
USA: $160
UK: £30
France: 54 EUR
Single-Entry, same-day processing:
USA: $300
UK: £90
Multiple-Entry, processing time 6 business days:
USA: $160
UK: £100
Multiple-Entry, same-day processing:
USA: $450
UK: £150

You could also do it through various private visa services that make the process easier, such as Visa Express