Main Verbs

Main verbs have meaning on their own (unlike helping verbs). There are thousands of main verbs, and we can classify them in several ways:

Transitive and intransitive verbs
A transitive verb takes a direct object: Somebody killed the President. An intransitive verb does not have a direct object: He died. Many verbs, like speak, can be transitive or intransitive. Look at these examples:

transitive:

I saw an elephant.
We are watching TV.
He speaks English.
intransitive:

He has arrived.
John goes to school.
She speaks fast.
Linking verbs
A linking verb does not have much meaning in itself. It "links" the subject to what is said about the subject. Usually, a linking verb shows equality (=) or a change to a different state or place (>). Linking verbs are always intransitive (but not all intransitive verbs are linking verbs).

Mary is a teacher. (mary = teacher)
Tara is beautiful. (tara = beautiful)
That sounds interesting. (that = interesting)
The sky became dark. (the sky > dark)
The bread has gone bad. (bread > bad)
Dynamic and stative verbs
Some verbs describe action. They are called "dynamic", and can be used with continuous tenses. Other verbs describe state (non-action, a situation). They are called "stative", and cannot normally be used with continuous tenses (though some of them can be used with continuous tenses with a change in meaning).

dynamic verbs (examples):

hit, explode, fight, run, go
stative verbs (examples):

be
like, love, prefer, wish
impress, please, surprise
hear, see, sound
belong to, consist of, contain, include, need
appear, resemble, seem
Regular and irregular verbs
This is more a question of vocabulary than of grammar. The only real difference between regular and irregular verbs is that they have different endings for their past tense and past participle forms. For regular verbs, the past tense ending and past participle ending is always the same: -ed. For irregular verbs, the past tense ending and the past participle ending is variable, so it is necessary to learn them by heart.

regular verbs: base, past tense, past participle

look, looked, looked
work, worked, worked
irregular verbs: base, past tense, past participle

buy, bought, bought
cut, cut, cut
do, did, done