Theory:

There are three ways of talking about the future in English, WILL, GOING TO and THE PRESENT CONTINUOUS.
For example:
I think I WILL eat fish tomorrow.
I am GOING TO eat fish tomorrow.
I am EATING fish with my sister tomorrow.

For each form, NOT is used to make the negative, and the same rules as those for the positive cases apply.

WILL - WILL NOT
So, let's start by looking at how to use WILL NOT.
WILL NOT is followed by the infinitive of the verb without TO, like I WILL NOT CALL YOU.
It is used for situations where you are not 100% sure, when you say I THINK.
For example:
I THINK he WILL NOT call. (You don't know for sure.)

This example is also a prediction, but without any evidence.
So WILL NOT is used if there is an element of doubt. (For a guess.)

GOING TO - NOT GOING TO
NOT GOING TO is used when you are sure, or have some evidence to justify what you are saying, like when you have already made plans.
For example:
I am NOT GOING TO speak to my boss. (You have made a definite decision.)
I know David is NOT GOING TO COME. (He called to tell me).

PRESENT CONTINUOUS
Finally, using the present continuous for the future.
I AM SPEAKING ENGLISH NOW is the present continuous.
It can also be used for the future, for plans that you have made and written in your diary.
It is very similar to GOING TO, but is not used for guesses, so it is different from WILL.
For example:
I AM NOT SEEING my dentist tomorrow. (I am sure because it isn't in my diary).