Calling back to the US from Moscow can be very expensive. Many people will advise you to use an internet phone card. These do offer low rates, but you will still have to pay high rates in the hotel just to connect to a local number when you use the internet phone card.
Another option is to use a US based international cell phone. This too will cost a lot - usually a minimum of $3 / minute and usually closer to $5 / minute.
There is a better way! The Ediniy pay-as-you-go plan from Megafon Moscow lets you call back to the US for 3R / minute (about 10 cents). Buy an inexpensive Russian cell phone. They are easy to find for less than $100. Or, bring an unlocked international GSM phone from the US. The Ediniy SIM card usually costs about 100R and includes 100R of calling time, so it is really free. You may need to have a Russian friend or colleague help you purchase the SIM card.
Add money to your phone at most ATMs, at the ubiquitous automatic cell phone kiosks or one of the many cell phone stores.
I've been using this approach for about 4 years and the call quality is good. You can also set the account up for data if you want to use it to surf the internet, check email or so forth.