We have all been through this question at one point or another. Do we say me or I when speaking? This is something I have always been confused about ever since I was young, but the major problem with this is that when the teacher tells us without actually explaining what is correct, we suffer through years of writing all the way through high school trying to figure it out. Honestly, I believe this needs to be learned at a young age somewhere around the same time when you're learning what verbs and nouns are.

I, he, she, and we will always be used before the verb.
|EXAMPLE| Rory and I are going to buy coffee at Luke’s.
In this example, going is the verb, so it would be Rory and I not Rory and me.

Me, you, him, and her will always be used after the verb.
|EXAMPLE| I think Ross just found out about me and Monica.
Ross found out. What did he find out about? About me and Monica, not Monica and I because the verb (found) comes before the subject.

|NOTE| Myself is hardly ever used and CANNOT be used as a replacement for I or me.

|EXAMPLE| 
I myself finished all of the work.
I completed the last of the group project by myself.

|EXAMPLE| Who do you think stole the car?
We use who because the question can be answered with he or she. I believe he stole the car?

Whom can be answered with him, her, or them.
|EXAMPLE| Whom is that present for?
We use whom because the question can be answered with him or her. The present is for her.