To find out whether to use ‘I’ or ‘me’, simply drop the name or pronoun that goes before and and the word and.
Then see if the sentence makes sense.
Example - I made dinner reservations for Rex and I.
Now drop ‘Rex and’ - I made dinner reservations for I.
Now this sentence sounds wrong, so you know it should be me. Let’s fix it - I made dinner reservations for Rex and me.
Bingo! Now it’s correct.
See full article and more examples at http://grammarpartyblog.com/2013/03/26/you-and-i-vs-you-and-me/