Use me after a preposition:
from me, to me about me, near me, by me, like me, with me, between me and you, against me (or against you and me)
When used with prepositions, me is the object of the sentence, while someone or something else is or does something:
She sat near me. (She is the one who sat.)
He is not related to me. (He is a non-relative.)
Use I for statements in which I am the one who is or does something (the subject of the sentence):
I ran a marathon and then came home and ate an entire cheesecake
I am a marathon runner and a lover of cheesecake.
The money should be split between you and me is correct; contrary to popular belief, you and I is not correct in sentences of this type because it is the money that is being split so the money is the subject of the sentence; you and me are just the lucky sentence objects that receive the money.
The situation becomes more confusing when a pronoun is proceeded by than because the meaning can change depending on whether you use I or me:
Jane likes hamsters more than I. (She likes hamsters more than I do.)
Jane likes hamsters more than me. (Jane prefers to spend her time with hamsters rather than in my company.)
Only use myself (or themselves, itself, ourselves, yourselves) for emphasis and self-reference.
Self-reference: He loves himself.
Emphasis: He loves his TV more than life itself.
When using these forms for emphasis, they can be left out without changing the basic meaning of the sentence:
He loves TV more than life. (This is a full sentence on its own.)
See the main Grammar, Punctuation, and Writer Resources pages for more tips and resources.
References:
- O’Conner, P. T. (1996). Woe Is I, the Grammarphobe’s Guide to Better English in Plain English. New York, G. P. Putnam’s Sons.
- University of Northern Iowa Department of Languages and Literature. (2012). “Frequently Asked Questions.” Dr.Grammar.org.