No expresses a general negative, such as when disagreeing, or indicates an absence of any of a particular noun.
No, I do not like coffee.
There was no coffee in his house.
(According to wikipedia): Not is the declarative form of no.
I'm pretty sure it classifies as an adverb, and negates the action of the verb in the emphatic form (do + verb).
I did not go to school today.
The train did not arrive.
