No is a determiner, it must precede a noun, and it will take the place of an article in things that can attach to a noun.
I took the ball from Suzy.
I took no ball from Suzy.
Exception is where no can be used to answer questions like yes.
No, I don't want to go.
I told him no. I'm not going.
Not is an adverb.
It can precede infinitives and gerunds.
I wanted him not running through my lawn.
Not to be difficult, but I think we should leave.
She was only concerned about him not going to the store.
But not present participles:
Go into the not running van and start it for me. (Wrong, has to be Go into the van that is not running ...)
Otherwise, an auxillary verb is required when using not and if one is not otherwise present, do is used:
I had gone to the park.
I had not gone to the park. (Auxillary there so just add "not.")
I had 2 pieces of candy.
I did not have 2 pieces of candy. (Had in the previous sentence is not an auxillary verb, so one is needed.)
The books were not stacked properly.
Someone not stacked the books properly. (Wrong. Sounds like a 2-year old learning to speak or a caveman.)
Someone did not stack the books properly. (Ok.)