Without context, it's not really possible to tell whether your example is correct or not. If you were labeling a photograph, for example, you could say: "This is Gerard and me at a party." But if you were telling someone that you are at a party with Gerard, you would say: "Gerard and I are at a party." Like Laurence has tried to show you above, removing the second person from the sentence is the best way to check your grammar. In my sentences, if I remove Gerard we have: "This is me at a party." Correct. If I had said, "This is Gerard and I at a party," once Gerard was removed from the sentence we would be left with, "This is I at a party," which is clearly not correct. "I am at a party." Correct. If I had said, "Gerard and me are at a party," once I removed Gerard from the sentence, we would be left with, "Me at a party," instead of "I'm at a party." You can always check your sentences this way so that, regardless of context, you know which option to choose.

Many, many natives get this wrong (including me all the time). The rules is: If you would say "I" without the other person there, then it's "my friend and I" Example: I went to the cinema yesterday Example: My friend and I went to the cinema yesterday Example: I'm sorry, I can't talk right now, I'm at a party Example: I'm sorry, I can't talk right now, Gerard and I are at a party (or "I am at a party with ___") Only these are correct. Many natives, including me, will often say "me and my friend went to the cinema yesterday". This is WRONG and try not to pick up this bad habit.

You need a verb first, let's say "met", and you have met with Bob. Once you have a verb, you can tell if your friend and you are the subject or the object of the verb. As Laurence says, the best way to figure out whether it is "I" or "me" is to forget about your friend for a bit (sorry!) You can also put "at a party" aside for a bit. Now we have either "I met Bob" or "Bob met me". In the first case, you are the subject (and Bob is the object), and in the second, it's the other way around. Now you can put this all back together again with the other stuff: "My friend and I met Bob at the party" and "Bob met my friend and me at the party".

It depends on the usage. "Me" is the object form. I is the subject form. If Gerald and you are the subject, use "I" --> For example, "Gerard and I danced at the party." If Gerald and you are the object, use "Me" --> For example, "Joe gave Gerard and me a drink at the party."

Technically, the correct way is to put yourself last. So "my friend and I" is more correct. But many native speakers do not do this. You will be understood either way.