Wes, a very intelligent and articulate former co-worker of mine, once asked me, “When do you say ‘Grace and I’ and when do you say ‘Grace and me’?”
 
Unlike many lessons in the complicated English language, this one is fairly easy to learn and remember.  When speaking of yourself and someone else, pretend you are speaking only of yourself, and use the appropriate pronoun.  Since “I am going to the store,” and not “Me am going to the store,” then it is simply “Grace and I are going to the store.”  Likewise, if “Wes gave a Christmas card to me,” then “Wes gave Christmas cards to Grace and me.”
 
Without exception, the subjective pronoun “I” is used at the beginning of sentences, as in “I smile at my neighbors.”  If you start your sentence with “Grace and . . .,” it is going to start with “Grace and I . . .” when you add yourself.  There is no instance when beginning a sentence with “Grace and me . . .” is correct.
 
In most cases, the objective pronoun “me” is used at the end of a sentence, as in “My neighbors smile at me.”  Therefore, most sentences where you include yourself at the end will conclude with “. . . Grace and me,” however, there is a catch to this.  While there is no proper way to begin a sentence with “Grace and me,” there are legitimate occasions when you will end a sentence with the subjective pronoun “I.”  An example is “No one knows the people of this town better than I.”  The reason for this is because you are putting yourself in the position of the subject of the sentence “No one.”  What you are really saying is an abbreviated form of the sentence “No one knows the people of this town better than I know the people of this town,” so if you drop the verb from the end of the sentence, it remains “. . . better than I.”
 
In fact, the common phrase “Woe is me” is grammatically incorrect!  It should be “Woe am I,” because you are saying a fancy version of “I am sad.”  “Sad am I,” though a bit dramatic, is technically correct.
 
These are all good things to keep in mind the next time you feel compelled to exclaim, “Woe am I!  Wes knows the people of this town better than Grace and I, and he didn’t give Christmas cards to Grace and me this year!”