If you're an American (and many other nationalities, as well), you'll need not only a passport but a visa from the Russian embassy (there are several in the US -- which one you need depends upon which state you live). And to get a visa, you need an "official" invitation from someone in Russia. I've been to Russia several times, but the first time is quite daunting, as the paperwork involved is a bit of a hassle.
Unfortunately, many of the above answers are incorrect. If you're an American (or someone from western Europe -- I do not know about other countries), even if you'll only be in Russia for a day, you will need a visa! Also, whoever said that whenever you travel out of the travel, you need a visa is simply wrong. It depends entirely on the country. I travel to Europe multiple times per year and only take my passport. However, some countries do require visas for Americans. Russia is definitely one.
Edit: I see your additional information. Since you're a US citizen, it really shouldn't be difficult to get a visa, but do it at least two months before your intended travel. Russia is wonderful, but be prepared -- everything takes about twice as long to accomplish as we're used to doing.
If you live in Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, or Vermont, the Russian consolate in New York will issue your visa. Go to http://www.ruscon.org/ and click on "entry visa to Russia."