Me is an object pronoun while I is the subject pronoun. I read a great tip on Literary Rambles last week for how to remember I vs. me using math. Read Dale's tip here.
The Cliff's Note version:
- Subtraction: I or me can be confusing if the subject or object is more than one thing. Subtract the additional person to find the answer.
"Joe and me ate pretzels until my belt buckle burst." "Joe and I ate pretzels until my belt buckle burst."
Take out Joe and it's easy to recognize that I is the correct choice because I is the subject of the sentence.
- Addition: Add in the assumed portion of the sentence to find the correct pronoun.
Add what they're doing. "He and I are going to a party." "He and me are going to a party."
The first one is correct.
If I got anything wrong, feel free to correct me in the comments. Are you doing the A to Z challenge? Let me know and I'll come check it out.