A word is usually (not always) the subject if a verb comes after it. Adverbs, appositives, etc. can also go before a verb, but it is still not a noun (I'm not sure if you learned these so I will not talk about them too much).
Subjects are never in the prepositional phrase. The subject is always the word or words that are doing an action or receiving an action.
example: Henry kicked the ball.
Who is doing the action (who is kicking the ball)? Henry is kicking the ball, so Henry is the subject.
example 2: Jack ate a sandwich in the kitchen.
"in the kitchen" is the prepositional phrase
Who ate the sandwich? the kitchen did not eat the sandwich, nouns are never in the prepositional phrase
Who ate the sandwich? Jack ate the sandwich, Jack is the subject
example 3: Susie, the dog, slowly walked into the house.
"walked" is the verb
the verb "walked" is right after the word "slowly"
do not be tricked, "slowly" is not the subject, "the dog is not the subject"
the word right before a verb is not always the subject
"Susie" is the subject