You will find that almost every chain retailer or restaurant accepts cards, and many other businesses do as well. This is especially true in Moscow and St. Petersburg. Master Card, and Visa are the most commonly accepted forms of credit or debit payment.
You should expect to pay in cash for taxis, at street vendors. Luckily, Russia is well-outfitted with ATMs. You will get the same exchange rate at an ATM as you would at an official money changer, so this may be your best bet if you'd prefer not to bring cash into the country.