Quick answer
Будь здоро́в!
but zdaróf — literally “be healthy” — and it changes with who sneezed
The options
Будь здоро́в!Bless you! — to a man, informal
Будь здоро́ва!Bless you! — to a woman, informal
Бу́дьте здоро́вы!Bless you! — polite or plural
Спаси́бо!Thank you! — the reply
Не боле́й!Don’t get ill!
The forms
It is an imperative of быть plus a short adjective, so both parts agree: будь здоро́в (to a man), будь здоро́ва (to a woman), бу́дьте здоро́вы (polite or several people). Getting the gender right is noticed.
Sneezing superstitions
Some people count sneezes, and a sneeze while someone is speaking is taken as confirmation that what was said is true: Пра́вду говорю́!. If a child sneezes, an older relative may add расти́ большо́й — grow up big. None of it is taken very seriously, but all of it is said.
What you hear back
Спаси́бо!Thank you!
Спаси́бо, уже́ лу́чше.Thanks, I’m better already.
Да, просту́да.Yes, a cold.
Typical mistakes
Будь здоро́в — to a woman
Будь здоро́ва.
The short adjective agrees.
Бог благослови́т
Будь здоро́в!
Russian wishes health, not a blessing.
Check yourself
A woman sneezes. You say:
Feminine short form.