In our time of flexible yield management, the concept of ticket sales is a little outdated. For example, you are looking at a flight from New York to Singapore, and United shows the current price of about 1000, in a couple of days an absolutely identical flight will cost 600, and in another day 1200. Check regularly, on sites like Google flights, which allow you to quickly check the price for any direction. Sales are more of a marketing ploy now, and with rare exceptions, when you click on a link that promises extra cheap tickets for your dates, there is nothing. The most important factor to save money is flexibility with dates, at least within 2-3 days.
It seems - none. Well, or I don't know this.
The fact is that airlines have sales when they need to load seats on their planes. This usually happens during low season when fewer passengers are flying. In Russia, this is traditionally the winter season from November to March, with the exception of New Year's holidays. At this time, they fly less and in order to somehow compensate for these losses, airlines are holding sales, hoping to get those customers who would not fly, and at the same time money for future flights.
At other times, in the high season, in summer, such a tactic is unprofitable, since a seat on the plane will still be bought, and at a high price (due to the huge demand), so there are no sales in summer. The exception is new destinations, but some new flight to a new city does not attract a global sale.
So don't look for a specific carrier - everyone arranges a sale when they need it. Visit airline websites and follow profile blogs. Then don't miss the sale for sure)
All airlines in one way or another come up with some kind of marketing moves, including sales. If you follow the statistics, it is easy to notice that the conventional Aeroflot organizes two really big sales every year, and AirBerlin gave the second ticket for Valentine's Day free of charge.
The surest way not to miss the sale is to subscribe to the mailing lists of the airlines of interest.
If you do not take any special offers or errors in the tariff setting systems, then traveling as inexpensively as possible from Moscow is possible with:
with Pobeda Airlines flights (Barcelona, Bratislava, Milan, Cologne, etc.)
with S7 Airlines flights at the Economy Basic fare, in this case without baggage and the possibility of returning a ticket, but, indeed, inexpensively for interesting destinations for direct routes - Genoa, Alicante, Mallorca, Naples, Verona, etc.
you can also start your journey with a flight from Moscow to Budapest with Wizzair. And then it is easy and inexpensive to fly to any corner of Europe using low-cost airlines. Or use inexpensive bus routes (say, from Budapest to Prague or Vienna), because there is also a low-cost bus in Hungary - Orange ways.
Traditionally, due to the high competition and high frequency of flights, the cost of flights to Germany is significantly lower than neighboring countries.