When do use I and when do you use me?

I is a subject pronoun, so it goes before the verb:

I saw him. saw = verb / him = object.

Me is an object pronoun so it goes after the verb:

He saw me. saw = verb / me = object.

Other examples ( verb is bold):

Jack and I went to the cinema. My brother and I know karate.

My little brother kicked me. They chased me.