Santé! Prost! Skål! Cheers! One of the beautiful facts of humanity is that no matter how different our cultures may be, some things are universal. It doesn't matter if you're drinking beer in Poland, rice wine in Vietnam, or whiskey in Ireland -- when it's time to raise a glass in toast, there's always some form of tradition to follow. At a minimum, toasting etiquette usually involves repeating a word or short phrase in unison.
In Russia, a standard toast requires raising and clinking your glass –- commonly a shot of vodka –- with your companions and saying "vashe zdoroviye." Pronounced VAH-sheh zda-ROH-vee-yeh, the saying roughly translates to "for your health." In fact, you'll find that most countries' toast words mean some variation of the same phrase.
Russians take their toasting seriously, so while saying vashe zdoroviye over a glass-clink is sometimes all that's necessary, it's not uncommon for there to be much more ceremony. Often, the toast-giver will give a speech first, whether it be an homage to an individual or simply an entertaining story. It's considered rude to eat, drink, or hold your own conversation during the toast, so everyone is expected to give their complete attention.
It's also impolite to refuse to participate in a toast, as it can imply a lack of respect for the subject of the tribute. Read more: Clinking your glass and saying "vashe zdoroviye" will prevent you from making a social faux pas at a Russian gathering. However, if you want to pass.