Me and John are going to the store. WRONG. How do I know? Take out John and you get:
Me is going to the store. Clearly WRONG, right? So, the correct way to say it is:
John and I are going to the store.
Most of us have been corrected on that particular usage error so many times that some of us begin throwing "I" in willy nilly anytime "me" feels like the right word. The problem: sometimes "ME" is correct! And now, aye yi yi, people trying not to make a mistake are blowing up grammar to the extent that a patently wrong word usage is beginning to sound right and even *smart*. Shudder. Some examples to help you navigate the waters of 'me.' Remember, if you're not sure, just take out John!
Do you want to go to the store with John and I? WRONG. Check it out. Take out John and you get:
Do you want to go to the store with I? Blech, right? We can all agree? So, correctly stated:
Do you want to go to the store with John and me?
That's right, the word 'me' is just out there proudly waving its object flag.
Let's keep this between you and ME.
Give John and ME a hand with this.
Picture tagging is one area where the fear of 'me' has scared people silly. You look at a picture of two people and then you read the tag: John and I. WRONG. It's not quite so obvious when you take out John, but what would you think if you saw a picture labeled "I." Clearly wrong, right? Remember that the unstated preface to the phrase is "This is a picture of...." which makes the entire phrase one big OBJECT of a preposition.
John and I at the Grand Canyon. WRONG
John and me at the Grand Canyon.
If you switched things around and made these phrases the subject of the sentence then you WOULD say "John and I were at the Grand Canyon." Notice that verb in there? Changes everything.
But just keep it simple. When in doubt, take out John and say the sentence again. How does it sound?