Generally the water in Moscow is not dangerous, but it's best not to drink it straight from the tap. In comparison, the water in St. Petersburg is so polluted that it is not even safe to rinse with it while brushing your teeth.
Most Muscovites drink the water after boiling it.
Westerners generally use some form of filtration system or buy bottled water from a company that delivers to their home or office, or purchase it by the case at the supermarket. You can prepare and store tap water for drinking by boiling it for 20 minutes and then filtering it using a Brita or similar filtration system. Water filters are available in many housewares stores and rinoks.