"Familiar to" and "Familiar with"

Familiar with = well informed about or knowing thoroughly. 
or talking to someone as if you know them well although you do not

• Example:

Are you familiar with the problems that usually arise in this shop?

I'm sorry, I'm not familiar with your poetry. 

You are (not) familiar with astrology.

• Familiar to = recognizable. 

The street was familiar to me.

 Astrology is (not) familiar to you.

• In easier way you can understand like this

The people are familiar with something.

Something is familiar to the people.