The most common mistake foreigners make when they try to propose a toast in Russian is “НА здоровье”. Actually it is very clear what they mean when they say this but you will never hear it from a Russian native speaker. Russians always drink ЗА (for) something. So we use the preposition “за” (not на).
So next time when you are going to celebrate something with your Russian friends surprise them saying the toast as perfectly as native speakers do – say, “За здоровье!”
And by the way health is not the only one thing Russians can drink to. You can also drink to:
За здоровье! – to health!
За любовь! – to love!
За богатство! – to wealth!
За успех! – to success!
За дружбу! – to friendship!
За Вас! – to you!
За нас! – to us!
ЗА – whatever but don’t forget to use the accusative case after “за”. More about the Accusative case