Learn English – Transitive verbs VS intransitive verbs

I dreamt a strange dream.

The verb dream can be used as a noun, transitive verb, or intransitive verb. In the above sentence, it's a transitive verb; the subject is I and the direct object is "a strange dream". The sentence, though grammatically correct, sounds old-fashioned. Usually, you say "I had a strange dream.

All his friends laughed at him.

The phrasal verb in the sentence is a transitive verb; the subject is "all his friends and the direct object is "him".

The watch cost nine hundred dollars.

The verb is transitive; the subject is "the watch" and the direct object is nine hundred dollars.

Unfortunately, Ghanshyam, for non-natives like us, there is only one way to learn things in English. Memorize them. Especially for Indians where we have our own rules to amend the language, there is nothing we can do. Just observe native speakers and their styles and you learn. That's it.

Well, now here, it's an intransitive verb. True. That's because transitive verbs requires something to transfer! [I remember that way -transitive transfer, intransitive, no transfer, thanks grammargirl]

Said that, intransitive verbs can stand alone without any support. They won't look odd. Say--

He ran

the sentence is fine without any additional information.

But then...

I want

is 'half'. You want 'what'? So, here, the verb 'want' is transitive which requires something to transfer. You add 'what you want' and it is a complete sentence. They call it as an object.

I want a car

In your example,

An old baggar[sic] stood (by the gate)

'by the gate' is an additional information but not necessary to complete the sentence.

Hence, they mark it with 'intransitive'.

The verb 'stand' is both transitive and intransitive but in its general (and most of?) usages, it's 'transitive'. More information is on OALD.