Quick answer
Спаси́бо
spasíbo — the everyday thank you, in every situation
The options
Спаси́бо.Thank you. — always right
Большо́е спаси́бо.Thank you very much.
Спаси́бо большо́е!Thanks a lot! — same words, warmer
Благодарю́ вас.I thank you. — formal, a little old-fashioned
Спаси́бо за по́мощь.Thanks for the help. — за + accusative
Where спаси́бо comes from
It is a contraction of спаси́ Бог — “God save you”. Nobody hears the religion in it any more, but it explains the odd shape of the word.
What you hear back
Пожа́луйста.You’re welcome. — the standard
Не за что.Don’t mention it. — literally “there is nothing for it”
На здоро́вье!You’re welcome — after food, not a toast
Всегда́ пожа́луйста.Any time.
Typical mistakes
Спаси́бо ты
Спаси́бо тебе́
The person thanked goes into the dative.
На здоро́вье as a toast
За здоро́вье! / За встре́чу!
На здоро́вье is what a host says when you thank them for food. Toasts start with за.
Check yourself
Someone thanks you. What do you answer?
Пожа́луйста means both “please” and “you’re welcome”.