When you are negating with *not*, look at the finite verb in the clause, the one that carries person and tense. 

 - If it is an auxiliary verb (the first verb in a verbal construction) or a form of *be*, you may simply add *not*:
 > He is here. ... *The verb is a form of **be***. >>> He is not here.  
 > He has arrived. ... *The verb **has** is an auxiliary*. >>> He has not arrived.  
 > He must have arrived. ... *The verb **must** is an auxiliary*. >>> He must not have arrived.  

 - Otherwise, you require *DO-support*:  
 > He came today. ... *The verb **came** is not an auxiliary*. >>> He did not come today.  
 > He arrived today. ... *The verb **arrived** is not an auxiliary*. >>> He did not arrive today.  
 > He has a car. ... *Here **has** is not an auxiliary but a lexical verb meaning 'possesses'*. >>> He does not have a car.  

Until the twentieth century it was common to negate lexical *HAVE* without *DO-support*, but this is disappearing. Even earlier **any** verb might be negated without *DO-support*, but that died out by the nineteenth century.