Many people use I and me interchangeably in conversation and nobody minds. People care more in written communication so here are some rules.

I = subject of a verb.

I (subject) looked at him (object).

Me = object of a verb.

He (subject) looked at me (object).

Many people use these pronouns correctly when they are just talking about themselves, but go wrong when another person is in the sentence. For example:

They were teasing her and I about going back. (incorrect – her is the object of the verb ‘teasing’, therefore I should be me, the other object of the verb)
They were teasing her and me about going back. (correct)

Michelle and me are making clothes for our dolls. (incorrect)
Michelle and I are making clothes for our dolls. (correct)

Sometimes it helps if you take the other person out of the sentence to see which pronoun you would use. That is the correct one.

I am making clothes for our dolls.

Out of respect, we usually put the other person first. These days it’s common for people to say, ‘Me and Benjamin went to the movies’; committing a grammatical error and also being impolite! The correct version is: ‘Benjamin and I went to the movies.’

Source: http://www.onlinegrammar.com.au/top-10-grammar-tips-i-and-me/

Photo: http://walkerediting.com/index.php/blog/me-and-i-personal-pronouns/