Verbs

We can talk about verbs in various ways:

Voice

Active voice:  The subject of the sentence performs the action.

The old woman carried a pail of water. 
[The subject, the old woman does the carrying.]

Passive voice: The subject of the sentence receives the action.

A pail of water was carried by the old woman. 
[The subject, the pail of water receives the action.]

More complete advice on the passive voice.

Transitive, Intransitive, and Linking Verbs

Transitive verbs
Transitive verbs require a direct object; the subject performs an action on someone or something.  
The direct object answers the question what or who.
The direct object doesn't have the word to in front of it.

The vampire opened the castle window.
[The vampire opened what?  the window.]

Sometimes the transitive verb may also have an indirect object, a noun or pronoun that answers the question to whom or to what. The word to may or may not be used.

The scientist gave the vial to his assistant.
The transitive verb is gave; the direct object is vial; and the indirect object is his assistant.

Sometimes the indirect object comes before the direct object, especially when the indirect object is a pronoun.
The scientist gave him the vial. 

Both the direct object and the indirect object are in the objective case.

The passive voice (see above) can only be formed from transitive verbs.  

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Intransitive verbs
Intransitive verbs do not take objects.
The water evaporated.
They may be followed by other words, especially adverbs or prepositional phrases.  Instead of answering the question what, these words answer questions like where, when, or how.

The water evaporated quickly. [Quickly is an adverb.]
The water evaporated from the kettle. [from the kettle is a prepositional phrase]

The train arrived late.

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Linking verbs
Linking verbs do not express an action at all.   Instead, they link the subject to a noun (or noun phrase) or to an adjective (or adjective phrase).

If you use linking verbs too much, instead of action verbs, your writing will lack vitality. 

The verb to be is the most common linking verb.  Some others are appear, become, feel, grow, look, prove, remain, seem, smell, sound, taste, turn.

The meat appears spoiled. 
Hamlet was king of Denmark. 

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Auxiliary verbs

Mood

Tense

Verbals: Words that look like verbs--but are actually other parts of speech.