a letter of confirmation of booking and pre-payment of accommodation and travel arrangements in Russia. It is accompanied by a tourist voucher. These two documents can be issued by "government approved" tour operators, hotels, online hotel booking services or Russian travel agencies (several Russian travel agencies have offices outside Russia and are adept at facilitating visa applications). "Government approval" here means that the organization in question has a "consular reference" and has been registered with the Russian Ministry of Foreign Affairs. Only hotels and travel agencies that have a consular reference can issue confirmations valid for visa purposes. An ordinary hotel booking is not sufficient to constitute an invitation. Some hotels charge a fee to issue the invitation.
Booking one night in a hotel will get you an invitation valid for one day (maybe two) and hence the resulting visa will be valid for a very brief time. For independent travellers planning to travel around Russia, it is best to get an invitation through an agency. These agencies will issue a confirmation for a fee (approx. $30 or £15), without actually collecting the accommodation prepayment. While the strict legality of such is questionable, it is a largely academic point and does not leads to problems for the traveller. If your itinerary is confined to only one hotel, then it makes sense to obtain the invitation documents directly from the hotel as the service fee will be similar.
Consider getting a private/homestay visa if you have friends or relatives in Russia (they do not necessarily have to be Russian). They would need to seek an invitation through their local Passport and Visa Division of the Federal Migration Service (formerly OVIR). These invitations tend to take at least a month to process. The inviting individual also becomes solely responsible for all your activities while in Russia and can be penalized heavily if something were to go wrong. Because of this,
