The good news is that almost everyone is familiar with Russian word Спасибо. This is a contraction of the phrase спаси Бог (may God protect you). Over the centuries wishing someone God's deliverance became the way to thank them.
It can be personalized: Спасибо Вам (formal), Спасибо тебе (informal). It also can be Большое спасибо! (A great big thanks).
Another word for gratitude is благодарность (noun) or Благодарить/ поблагодарить (verbs). Благодарность comes from the word Благо, something that's good or useful and Дар (gift, sacrifice). The original word seems to have been borrowed from Greek word for Eucharist, the giving of thanks (literally, «good favor»).
In a formal way you can say: Благодарю Вас. Or: благодарю тебя (informal). Or: Я очень благодарен/ благодарна за вашу помощь. (I'm very grateful for your help.) In very formal speech we can use verbs Выражать / выразить БЛАГОДАРНОСТЬ: Мне хотелось бы выразить благодарность за вашу поддержку. (I would like to offer my gratitude for your support.) There is also adjective благодарный (mas.) to describe something rewarding, I.e., something for which you can be grateful. Работа со студентами - благодарный труд. (Working with students is rewarding.) If you're feeling quite formal, you might say: Я Вам очень признательна/признателен. (Much obliged to you). If it were the 16th century, you might use the expression бить челом, which means «to beat one's brow. » This comes from the ancient Russian custom of bowing low and touching one's brow to the ground when petitioning or thanking the prince or tsar. This kind of expressions are pretty archaic and not common in a modern Russian language. But of course, they exist in a Russian fairytales and epic stories.
