Analyze the following scheme, point out the elements of the sentence and the predicative construction. Compare it to the scheme of the same construction with the Infinitive

Don't eat me. I have a wife and kids! Eat them! (Homer Simpson)

(Step 1: Find the verbs. Verbs = don't eat, have, and eat)
(Step 2: Ask "what?" for each verb. Q: Don't eat whom? Have what? Eat whom? A: me, a wife and kids, and them)

The verb could be a phrasal verb (e.g., to put down, to give up, to recover from).

• 
  My cat is recovering from a massive stroke. (Comedian Darren Walsh)
  

(Step 1: Find the verb. Verb = is recovering from)
(Step 2: Ask "what?". Q: Is recovering from what? A: a massive stroke)

It can get complicated.

• 
  The cat wants to eat our goldfish.
  

(Step 1. Find the verb. Verb = wants)
(Step 2. Ask "what?". Q: Wants what? A. to eat our goldfish)
(That seems easy enough, but note that the direct object has its own verb and direct object. (Q: Eat what? A: our goldfish.))

Don't forget that the term noun does not usually mean a single word. An object can be a single-word noun (e.g., dog, goldfish, man), a pronoun (e.g., her, it, him), a noun phrase (e.g., the doggy in window, to eat our goldfish, a man about town), or a noun clause (e.g., what the dog saw, how the goldfish survived, why man triumphed).

Read more about direct objects.