After sorting out your Trans-Siberian tickets, you need to get your visas. How to arrange a Russian visa...
Always check the latest visa information, as it changes from time to time. But here's a quick run-down of the arrangements as at 2007:
Tourist, transit or business visa..? A tourist visa allows stays of up to 30 days, and is probably what you need. A business visa allows a longer stay, but is more expensive. A transit visa allows up to 10 days in transit, but you aren't allowed to spend time in Moscow (as most Trans-Siberian travellers do).
When to apply..? Visas are only issued 90 days or less before your intended date of entry to Russia, so no need to apply before than. Ideally, allow a month for the visa processing, but if you have less time than this, don't worry, various agencies offer 'express' services that will help you get a visa much quicker.
Letters of invitation & visa support: A hangover from Soviet times is that to get a visa you need supporting documentation ('visa support'). In theory, this must be a letter of invitation from your travel agency, or for independent travellers, an accommodation voucher from your hotel(s) covering every night you plan to spend in Russia. This is ridiculously restrictive, so here's how it really works: You go to an agency such as www.realrussia.co.uk or one of the Russian agencies listed above and they sell you the necessary visa support for a small fee, which allows you to get a visa without any hotel bookings, so you can travel freely just as you would in any other country. Behind the scenes, this usually works by the agency having an arrangement with a local hotel, and a 'reservation' is made for you so they can legally issue the visa support, even though you don't pay for the hotel and everyone knows (apart from the Russian government) that you have no intention of ever using that reservation.
The simple way to get a Russian visa: If you live in the UK, the easiest and quickest way to get a Russian visa is to use www.realrussia.co.uk. Real Russia is a reliable UK agency which arranges Russian visas simply and cheaply, including all necessary visa support included in the price shown on their site. They have already recommended by one seat61 correspondent. Seat61 gets a small commission if you buy through www.realrussia.co.uk using this link. www.realrussia.co.uk can also arrange Chinese and Mongolian visas, and train tickets too. If you have feedback on their service, please email me..!