Russian currency is, of course, rubles, and all the payments conducted in Russia are made in rubles. You can exchange dollars for rubles in any bank, often in your hotel, plus there are money exchange offices throughout the city, virtually on every corner. Their rates may slightly differ, but not much. If you are approached by a person offering to buy dollars from you for a better rate, refuse. It is very likely that you will be scammed.
Major credit cards are now accepted in Moscow by most stores and hotels. Unfortunately, credit card fraud is not uncommon in Russia, so it is probably better to get money through ATM’s (they are widely available as well) and use cash. You can also bring traveler’s checks and cash those.
Service
If you know anything about the Soviet era service, you know it’s bad. There actually used to be two types of service: one for the Russians, and one for the foreign visitors. The one for foreigners was tolerable (even the Soviets realized that they’d quickly lose all the foreign tourists if they don’t treat their visitors well). The one for the locals was downright horrible. The Russians are people of immeasurable pride; Communists fed it, and had taught the people to see serving others as something disgraceful. Being nice to a customer was viewed as being servile, and no proud Russian would lower themselves to that. Clerks, sales assistants, and hotel personnel hated their jobs and their clients, and used to be notorious for rudeness or even trying to boss the clients around. Thankfully, most of that is now in the past. You may still bump into a leftover of the Soviet system in the form of a rude or indifferent clerk, but good stores and hotels now value their reputation and provide decent customer service.