me, myself and I
Okay, first off, 'myself' is not a synonym for 'me.' My brother and I watched Transformers. That's correct. Equally correct is: I and my brother watched Transformers. 'I' refers to the first person singular. When the first person singular is the subject of the sentence, always use 'I.' Think about it, you would never say. "Me is watching the Transformers." It would be, "I am watching the Transformers." When you are the object of the sentence, however, use 'me.' My brother handed the Optimus Prime figure to me. Mom handed the action figures to my brother and me.
"Whoa," you say, "What if you buy yourself a movie ticket? Should it be, 'I bought me a movie ticket,' or 'I bought a movie ticket for me'?" Neither. It's, "I bought myself a ticket" or "I bought a ticket for myself." Here, you are not the object of the verb. The 'myself' is what's called a reflexive pronoun, i.e. it's referring back to the subject.
By the way, remember when I wrote "My brother and I watched Transformers" and "I and my brother watched Transformers" are equally correct? Grammatically they are. The former, however, is more polite.