The best way to find the subject of a sentence is to find the verb first. After you found the verb, ask "Who?" or "What?" in connection with the verb. Frequently the sentence base will have not only a subject and a verb, but also a complement. A complement completes the meaning begun by the subject and the verb.
A predicate noun is one kind of subject complement. It is a noun or pronoun that explains or identifies the subject of the sentence.
A predicate adjective is another kind of subject complement. It is an adjective that modifies the subject of the sentence.