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Two you-s

When you address a Russian in Russian there are several things to keep in mind. First come the pronouns:
“Ты” is reserved for a friend or a kid. It’s also O.k. to address an unknown young person with “ты”, e.g., if you are both students. And don’t be surprised if a much older person whom you don’t know addresses you with “ты” – age has its privileges. If an older person addresses you with “ты” it doesn’t automatically give you a permission to do the same to them, unless they allowed you or asked you to do so.
“Вы” is for everyone else if you want to be polite and/or formal. If you don’t know a person, it’s better to start with “вы” even if you are the same age, and then one of you can offer to “shift to ‘ты’” – “перейти на ты“.

Using first names

If you are on a “ты” basis with someone, it means you will call them by their first name only. Usually, you will use the short version of their first name (Masha instead of Maria), but if you want to retain some formality in spite of your equal age and status, you can keep using the full version of their name (Maria, Olga…).

Another step in the formal direction would be to use the full first name and “вы.” A typical situation here is a conversation with a hardly known person or a boss who is the same age as you.

Using patronymics

Even more formal and very polite address would be a combination of “вы” and full first name + patronymic. Remember: Never use a first name-patronymic address with “ты.” And don’t combine a patronymic with a short version of a first name: It’s “Мария Ивановна“, not “Mаша Ивановна.” Nowadays, patronymics seem to be in decline: It’s hard to remember them, they are sometimes too cumbersome to pronounce, so using a full first name with “вы” will also be fine, especially if a person is not much older than you.

Using surnames

At last, the most formal (but not necessarily most polite) way of addressing a Russian is to use “вы” and to call him by his surname adding a Russian version of “Mister” or “Missis”. Earlier, it was “това´рищ Иванов” (comrade Ivanov), or “граждани´н Иванов” (citizen Ivanov). Now, “citizen” is still there and, as before, is used by the police or on similar unpleasant occasions, but tovarishch has been replaced by “господи´н” (m) or “госпожа´” (f) (lord, lady) which you’ll find mostly on official documents. It still sounds rather peculiar when used in the oral speech: One has difficulties to be called a “lord”, presumably, because one keeps asking oneself: A lord of what?