If you live in the west, especially in North America, chances are you go around a lot of the time with zero cash in your wallet. However, people in much of Eastern Europe and Russia still use cash most of the time, although credit card usage is growing every year. If you are traveling to Russia, here's what you need to know regarding money.
In general, just as anywhere else, you should only use a credit card in places that seem safe and trustworthy to you. Credit card scamming, skimming, and identity theft are widespread in Russia, as they are in the West, and so it is prudent to always carefully evaluate the place before you hand over a credit card. Most hotels and restaurants take credit cards, as do most establishments in large cities and generally accept MasterCard, Visa, and American Express. You will most likely not be able to pay for your taxi with a credit card, so always have some rubles on hand just in case.
Most ATMs accept international debit cards, and this is the best way to get cash in Russia. Many ATMs add on a fee if it isn't your bank, and some Russian banks add a second small fee. So it's wise to get as much cash as you think you'll need in one transaction and exercise the same caution at an ATM as you would at home.
Traveler's checks are not widely accepted in Russia, except at hotels and restaurants. If this is your preferred method of carrying cash, choose American Express checks, since most other types are not accepted across Russia. Traveler's checks were once ubiquitous when traveling in a foreign country since they are safer than carrying lots of cash and don't have to be exchanged. When you spend one you get the change in the country's local currency. Some people still find traveler's checks the most convenient and safest way to carry money when they are out of the United States, but there is actually little reason to use traveler's checks since you can get money from any ATM in Russia.
Cash is, of course, accepted everywhere. Its downsides include either taking a risk and carrying quite a lot of it or leaving it in a hotel room or running out because you take out small amounts from the ATM at a time. You should have a few rubles to pay for taxis, museums, tips, and the like, along with very small purchases. In general, it is safe to assume that you can use cash in Russia in much the same way as you do back home in the United States.