ВЫ vy* is more formal and used with people you don't know, people you just met, people you have respect for, or for many people (ex talking with your brother and sister ." you need to come here( вам надо там придти.))
Ты ty is used with close friends family animals even children whom you don't know. ex
сколько тебе лет? asking a child his age.
мне 8 лет. а вам? his reply (notice he uses вы form in dative case. it means that the person he is talking to is older and he shows this as sign of respect.
though kids use ty with their parents and family members they can be told to use vy with their older grandparents like great grandma's and grandpas
as a sign of respect.
Hello, dear beginner in Russian,
the Russian guy's explanation is pretty good, so I have just a tiny thing to add.
Vy and ty are pronouns and in Russian they have declensions .
There are six case but for now I guess it is good to remember the first three:
Nominative vy ty Inicial (like dictionary form) Who are you? Кто вы? Кто ты?
Genitive vas tebya Used as an objective I see you. Я вижу вас. Я вижу тебя.
Dative vam tebe Used like to whom. I give this flower to you. Я дарю вам этот цветок. Я дарю тебе этот цветок.
Hope it is not too overwhelming,