"I" is the subject form of the
first person personal pronoun. When a word is a "subject form" it
is used in the subject of a sentence.
E.g., I am going to
see Blade Runner at the Ridge Theatre tonight. My friend
John and I are going to see Little Shop of Horrors
at the Hollywood Theatre on Tuesday. (Not the often heard
"Him and me are going . . .")
"Me" is the object form of the
first personal pronoun. It receives the action or is the
object of a preposition.
E.g., John invited me
to the movies. John invited Fred and me to the movies.
(both direct objects) Give me a free ticket to the
movies. (indirect object). The conversation we had at the movies
was between him and me. (object of the preposition
"between")
In writing, make sure to avoid the
expression "between him and I," even though you will often hear it
on TV and radio.
Also, my pet peeve: He came to see
him and myself. Ouch! It seems to me the fear of not knowing the
difference between "I" and "me" has lead to the weird "myself"
usage. Learn the above and you will never have to make this
mistake again.