I always told my students that the subject of a sentence had to be a noun or a pronoun. Pronouns didn't usually bother them, because the basic subject pronouns are so familiar to us: I, you, he, she, it, we, and they.
Concrete nouns were no problem: tree, desk, pencil.
Sometimes they had problems with abstract nouns: freedom, anger, seriousness, difference
To make it really simple, I told them the following: If it isn't a what or a who, it isn't a noun and can't be a subject.
For instance, freedom is what we want, anger is what we sometimes feel, seriousness is what we need when taking a test, and difference is what sometimes exists between two thing.
When we started studying dependent clauses, it still worked in finding subjects.
"Who will be speaking is a mystery." What is the mystery???
Who will be speaking is the thing that is the mystery.
A noun = a what or a who A pronoun = a who
I hope this helps you with your grammar.
The subject of a sentence is the "thing or person" in the sentence doing the action. The object receives the action. The action is the predicate, or verb part of the sentence. Therefore, the subject can be a noun, a pronoun, or an "understood noun or pronoun". In some cases, an entire phrase or clause can act as the subject.
John bought the car for my birthday. "John" is a proper noun acting as subject, "bought" is the verb/action, and "car" is the object receiving the action. "Birthday" is the object of the preposition, 'for'.
Shut the door. The subject in this sentence is the understood "You". "Shut" is the verb, and "door" is the object receiving the action.
There are problems with this paper. In this sentence, "There" is a pronoun acting as the subject. "Are" is the verb, and "problems" is the object receiving the action. "Paper" is the object of the preposition 'with'.
Talking on the phone is my favorite hobby. The gerund phrase "talking on the phone" is the subject. "Is" is the linking verb.
I hope this helps clear things up for you...Good Luck!!