"I" can only be used as a SUBJECT (of either an independent or a dependent clause). It must always have a verb accompanying it:
I am hungry.
The coin that I found is very valuable.
"Me" can only be used as an OBJECT. It can me the object of a verb (either direct or indirect):
The shopkeeper gave me an exasperated look.
Or it can be the object of a preposition:
She went to the movies with me.
Between you and me, I thought the movie was terrible.
"Myself" should only be used REFLEXIVELY as an OBJECT. That is, it should only be used to describe things that one does to oneself.
I gave myself a haircut. It did not go well.
Compare this to:
She gave me a haircut. It did not go well.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education