Personal Pronouns: Should I use "me" or "I"? "Her" or "she"?

One point in grammar usage that people rarely question is when they say something like, "They were eating with Bob and I." This is actually an incorrect statement, grammatically speaking, of course.

We do this because we're always told to say "Bob and I" in any circumstance, but it's not always correct to say so. The difference lies in whether or not the people are the subject or the object in the sentence. For example:

Incorrect

Bob and me bought tickets to the game.

(subject) (verb) (object)

They gave Bob and I their tickets.

(subject) (verb) (object)

Correct

Bob and I bought tickets to the game.

They gave Bob and me their tickets.

My rule of thumb is if I can replace it with the word "we", then I use "Bob and I", and if I can replace it with the word "us", then I use "Bob and me."

If I converted the above sentences, this is how they would look:

Incorrect

Us bought tickets to the game.

They gave we their tickets.

Correct

We bought tickets to the game.

They gave us their tickets.

Likewise, people make a similar mistake when saying something like, "Her and her brother walked to the store." Imagine if the female's brother wasn't in the picture at all. You wouldn't be able to say "Her walked to the store." So, use a similar rule of thumb as above: if you can use "her" in the singular in the sentence, and it makes sense, then it's correct. For example, "He gave the book to her and her brother" can also make sense as "He gave the book to her." As you can probably guess, this also works for "he" versus "him."