There are two forms of address in the Russian language" "ты" [ty] and "вы" [vy]. It would be a mistake to suppose that the form "вы" [vy] is more formal than the form "ты" [ty]. In fact, both of them express politeness, if you use them in a proper way. If you all of a sudden use the form "вы" addressing the person who you have previously always addresed with "ты", it means you want to put some distance between both of you for some reason.
We use the form "ты" (you), when we address:
- members of our family
- children, even unfamiliar ones
- close acquaintance
- those who have agreed with us to "перейти на "ты"" [pireyty na ty] (go to first name terms).
We use the form "вы" (you), when we address:
- virtual strangers
- people who are significantly older than us
However, there are always some exceptions.
There are people, especially the older generation, who address children and teenagers with "вы".
There are people who address their age-mates, even unfamiliar ones, with "ты".
In most families children are raised so that they address familiar adults (e.g. mother's or father's friends) with "ты" - regardless of age disparity. It's quite acceptable.
It would be polite a priori to address a stranger with "вы". If you think you can close the gap because you have a liking for each other, want to keep in touch further, you are age-mates or prefer to keep it simple, - you can suggest to "перейти на ты" (go to first name terms) with the simple phrase: "Может, на ты?" [Mozhet na ty?] (Maybe we should go to first name terms?) or "Давай на ты" [Davay na ty?] (Let's shift to first-name terms) or "Не против, если мы будем на "ты"? [Ni protiv, yesli my budim na ty?] (Do you mind, if we keep names above titles?). Probably, you won't be turned down. But if you will, don't jump to conclusions (don't think that a person doesn't want to talk to you or doesn't like you). Perhaps, a person has another view of life or he/she feels at ease when he/she keeps the distance.
Young people usually address each other upon meeting with "вы" but it's not necessarily.