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.