What is a proper way to formally greet in the Russian culture?

I am seeing someone who grew up in Russia, but who moved here with her mother some 8 years ago. I wish to greet her mother formally, both culturally and in the native tongue. It would be something like the American/British equivalent of taking their hand and saying "Greetings, madam." Hopefully the general sense of what I am asking makes sense - the cultural differences do not line up, naturally.