• A finite verb is the form of a verb that shows
  Tense (Present/Past/Future, and all variants of those tenses)
  Person (first [speaker], second [spoken to], third [spoken about])
  Number (singular/plural)
  
• Non-finite verb forms have no person, tense, or number.
• For instance
  In the following sentences, the italicized verb forms are finite: I eat. You are eating. We ate.
  In the following sentences, the italicized verb forms are non-finite: He wanted to eat.  We were thinking about eating when we passed the restaurant.
• Some grammarians consider verbals to be non-finite verb forms.

• Transitive -- transitive verbs take a direct object or other complement.
  
  
  
  
  
  
  
  
• Intransitive -- intransitive verbs do not need a direct object for completion.

Transitive verb taking a direct object:
I ate my dinner alone.
(Ate is a transitive verb; dinner is the direct object.)

Transitive verb taking a complement:
I was hungry until I saw what we were having for dinner.
(Was is a transitive verb; hungry is the complement.)

Intransitive verb:
My dog came when I called him for dinner.
(Came is an intransitive verb; it does not take a direct object.)

• Verbs expressing action
  
  
  
• Linking verbs
  
  
  
  
  
  
  
  
• Auxiliary verbs:
  (Also known as helping verbs)
  [Note: Auxiliary verbs often take a participle (aka, main verb) to form a complete verb.]
  
  
  Auxiliary verbs refine the tense of a verb and express mood.
  
  
  
   

Action verbs are the most common and strongest.
Examples:  Explode, Dress, Congratulate

Linking verbs express a state of being or existence. They are not as strong because they do not convey a sens of action.
Example of linking verb expressing a state of being:  The meat smelled bad.
Example of a linking verb expressing existence: I am ready if dinner is ready.

Auxiliary or helping verbs cannot stand alone; they need a participle for completion:
We were finishing our dinner when the vampire came in through the window.
(Were is the auxiliary verb, finishing is the main verb (in this case, a present participle).

Vampires might enjoy garlic if they would give it a chance.
(Might and would are auxiliary verbs; enjoy and give are the main verbs.)

We were finishing our dinner when the vampire came in through the window.
(The main verb were finishing is in the past continuous tense.  In the sentence, We finished our dinner, the verb finished is in the simple past tense.)