To go to Russia, even just for a day, you need a visa. Most people will be fine with a tourist visa that lasts for 30 days, but the process to extend one is complicated and not clear for English speakers. There are also further steps to take in Russia to ensure that you can leave the country without trouble.
Plan ahead. It may take a while to get your visa, so be sure to allow yourself at least a month for the process. Before applying for a visa, research companies that can offer you an official letter of invitation, sometimes referred to as a visa support letter. It's simply a sheet of paper that says (in Russian) that you are welcome to enter the country. This must come from the Russian government and can take a few weeks to deliver. Make sure you have a passport that has two completely blank visa pages and is valid at least 6 months beyond your stay in Russia.
Order an official letter of invitation from a trusted company; these companies can be found online or through a travel agent. Have your passport and hotel reservations ready. Way to Russia is a major provider of tourist visas, processing thousands annually. The invitation will cost about $30 unless you need it expedited.
Apply for the tourist visa. The process varies by consulate, and you may need to travel a great distance to get to yours. Alaskans, for example, must travel to Seattle. Each consulate has its own rules, and while some require you apply in person, others prefer applications to be mailed in. Check with your local consulate to determine their regulations. Russian consulates in the United States are located in Seattle, San Francisco, New York, Houston and Washington, D.C. Plan ahead and apply at least 3 weeks before you depart. You can also apply through local visa or travel agents for someone to double-check your application and streamline the process.
Fill out a migration card at the border when you arrive, most likely on your flight or train. No one will tell you to do this in Russia, so you must do it independently. Be sure that your card is filled out with absolutely no errors or scribbles. If you make a mistake, ask your flight attendant for another. Make sure that both your passport and your migration card are stamped when you arrive and pass through customs, and guard that migration card with your life. If you try to leave the country without it, you could be detained and miss your flight, as well as face severe fines.
Register your visa. This is usually done by your host, most likely your hotel, but local travel agencies and the American embassy can also register your visa. If this is not done within 3 business days of arrival you can be fined. You'll receive a receipt proving your registration, which you must carry everywhere, along with your passport. Police perform random checks, and you must present your passport, visa and valid registration. You don't need to carry your migration card everywhere, though, as you will need that only to leave the county.