My number one grammar pet peeve is when people refuse to say "you and me" even when it would be the correct thing to say (they opt for "you and I" instead, because they have been wrongly informed by their 4th grade teacher that "you and me" is never correct).
A subject is someone or something that performs a verb (action).
An object is someone or something that a verb is happening to... or should I say... to which a verb is happening.
"You" can function as both a subject and an object.
"I" is a subject.
"Me" is an object.
In many cases, "you and me" is also preceded by a preposition, such as "between you and me" or "to/from you and me."
So, it is correct to say "you and I will go to the store," and incorrect to say "you and me will go to the store."
However, it is correct to say "they will be playing against you and me." It is incorrect to say "they will be playing against you and I."