When to Use "Me" or "I"

Gerson and I were having a conversation and I had asked him if he knew whether he knew the rule for "Me" or "I" in a sentence. He told me that the trick was to remove the additional person from the sentence and it would be obvious. Like the first sentence: "Gerson and I were having a conversation..." if your remove "Gerson" then it would read "I were(was) having a conversation..." If I were to have used me it would have read "Me were(was) having a conversation..." With this little rule it becomes self evident.