Complements are of four types:
Two are subject complements: predicate adjective and predicate nominative
The other two are: direct object and indirect object
The first two are used to modify the subject of the sentence.
The second two are complements that do not refer to the subject.
A predicate nominative is a noun or pronoun in the predicate that is used to explain or identify the subject, e.g. Tom is our guitarist. (p.n. = guitarist) The girl over there is she. (p.n. = she) A dog is a mammal. (p.n. = mammal)
The predicate adjective is an adjective in the predicate and modifies the subject. e.g. The sky is blue. (p.adj. = blue) The tea is cold. (p. adj. = cold) Our boss is mean. (p. adj.= mean)
As you can see in all six examples, subject complements ALWAYS follow a LINKING verb. (intransitive verb)
The direct object receives the action of the verb and answers the question: "What?" or "Whom?" after the action verb.
He threw the ball. (ball = d.o.) She dropped the plate. (plate = d.o) I will be buying milk at the store. (milk = d.o.)
Indirect object is the noun or pronoun preceding the direct object; it tells "to whom" or "for whom" the action of the verb is done.
Bob told Susan a long story about what happened. (i.o = Susan; d.o. = story) We will buy him a new bicycle. (i.o = him; d.o. = bicycle) My little brother sang me a song. (i.o. = brother; d.o. = song) I left you five dollars on your dresser. (i.o. = you; d.o. = dollars)
Direct and indirect objects follow an ACTION verb. (transitive verb)
Unfortunately, there's a lot more to complements in that all four types can not only be words, but also phrases and clauses. That's way too much to go into here. But what I wrote is the basic ideas and just keep referring to the rules to let it sink in.
One last thing about the verbs, some helping verbs can be linking verbs, and many verbs can be both transitive (action) and intransitive (linking).
Again, just keep reviewing these basic rules when reading or writing and it'll sink after a while.