In general, when looking for the cheapest flight to Moscow, try to choose a flight departing in January for the best deal.
From most locations, booking your flights to Moscow around 60 days prior to your departure date finds the best deals.
From most locations, the cheapest day to fly to Moscow is Wednesday. Most users found that departing on a Sunday was most expensive.
On average you can find the best deals on plane tickets to Moscow when looking for flights with afternoon departure times.