There are two kinds of linking verbs: those that express a state and those that express a result.
Express a state
am, is, are, was, were, be, being, been (any any combination that ends with be or been: has been, have been, had been, will be, shall be, may be, would have been, should have been, would be).
Express a result: These are called "resultative"
act, appear, be, feel, lie, look, remain, seem, smell, sound, stay, taste, become, get, grow, fall, prove, run, turn
A resultative verb can function as either a linking verb or an action verb. Here's a test you can use to help you decide: Replace the resultative verb with am, is, are, was, etc. For example, let's try the verbs 'grow' and 'look':
The man grows flowers.
=> The man is flowers. (Not OK)
('grows' is not a linking verb here. It's an action verb)
The man grows tired.
=> The man is tired. (OK)
('grows' is a linking verb here.)
She is looking at the flowers.
=> She is at the flowers. (Not OK)
('is looking' is not a linking verb here. It's an action verb)
She is looking good.
=> She is good (i.e., looking). (OK)
('is looking' functions as a linking verb here.)
Here's a test to help you decide whether the word that come after the linking verb is a noun or an adjective: Replace the linking verb with the verb seem. Only adjectives fit grammatically in the position:
He is a doctor.
=> He seems a doctor. (Not OK)
('a doctor' is not an adjective)
He is happy.
=> He seems happy. (OK)
('happy' is an adjective)