I'm having slight trouble determining if a verb is a linking verb, a transitive or an intransitive.

linking verbs do not express action. There are some verbs that are always linking verbs (like to be) and some that are on some occasions (e.g. look -> She looks very sad = linking verb; she looks at me = action verb).
The difference between transitive and intransitive verbs is that transitive verbs can be put in any form, while with intransitive verbs, some forms do not work (e.g. "arrive" cannot be used in the Passive -> "I am arrived" does not work, so "arrive" is intransitive)

only a few are linking verbs like is, are, seems, looks, smells, etc...
they're usually followed by a predicate nominal, that tells what the subject is or rename it (He is a boy) and predicate adjective (He looks sad) that describes the subject....

Transitive verbs are verbs with an object, or the action does something to an object. Better yet, ask questions what and whom. Ex. (He opened the gate. He opened what?)

Intransitive verbs are verbs without an object. (He came.) Some transtitive verbs can be intransitive though.Be careful cause sometimes a verb is followed by an adverbial phrase (He sang outside. Outside is an adverb of phrase.)