A verb must agree with its subject in number, person and gender.

Our followers are but a handful. (Here the plural verb are agrees with the plural subject followers.)
One of the boys was selected. (Here the singular verb was agrees with the singular subject one.)
He is an old friend of mine.

The subject must have a verb.

The subject of the sentence should be followed by a verb. Note that a sentence must have at least one verb. The following sentence is incorrect because it does not have a verb.

He who has won the prize, let him speak.

This sentence should be re-written as follows:

Let him who has won the prize speak.
OR
He who has won the prize should speak.

Infinitives

An infinitive should be in the present tense unless it represents an action prior to that mentioned by the principal verb.

I should have liked to win. (NOT I should have liked to have won.)
But it is correct to say:
He seems to have enjoyed his stay at the hill station. (Here the stay at the hill station took place earlier than the action mentioned by the main verb.)

The participle should not be left without proper agreement.

Consider the sentence given below:
Having bitten the postman, the farmer killed the dog.
The above sentence means that it was the farmer who bit the postman.
This sentence should be re-written as follows:

Having bitten the postman, the dog was killed by the farmer. OR The dog having bitten the postman, the farmer killed it.

Now consider the example given below:

Standing at the gate, a scorpion stung him. (This sentence means that it was the scorpion that was standing at the gate.) It should be re-written as follows:

Standing at the gate, he was stung by a scorpion. OR While he was standing at the gate, a scorpion stung him.

Constructions like these are, however, permitted in the following cases:

Considering his age and experience, he should have done better.
Roughly speaking, it would take around six months to learn English.

The verbs see, hear, smell and make are followed by noun/pronoun + plain infinitive.

They made the child drink the whole milk. (NOT They made the child to drink …)
I heard her sing a lovely song. (NOT I heard her to sing …)

The verbs enjoy, avoid, miss, postpone and suggest should be followed by gerunds, and not to-infinitives.

She enjoys singing. (NOT She enjoys to sing.)
Mother suggested consulting a doctor. (NOT Mother suggested to consult…)