Which is correct: 'John and me are going to work' or 'John and I are going to work'?
The first is common, but the second is correct.
How do you tell? It's easy.
Split the ideas into two sentences. Would you say 'Me am going to work? Then it's the other one: 'I am going to work' - and John is going to work'. (You'll need the plural 'are' when you are talking about both of you.)