The nai-form: making negatives
The nai-form is the basic plain non-past negative of a verb. Pay attention to changes such as 買わない and こない, then connect the form to negative past statements.
Group 1: move to the a-row
Change a group 1 verb's ending to the a-row and add ない: 書く → 書かない, 読む → 読まない, 話す → 話さない. Simply replacing ます with ない can produce incorrect forms such as 読みない.
For verbs ending in う, use わ rather than あ: 買う → 買わない and 会う → 会わない. 帰る is group 1 and becomes 帰らない; do not simply remove its final る.
Group 2 and special forms
For group 2, remove る and add ない: 食べる → 食べない and 見る → 見ない. The irregular forms are する → しない and 来る → 来ない（こない）. Distinguish the き in 来ます from the こ in 来ない.
The ordinary negative of existential ある is ない. 机がない means there is no desk, while 人がいない means there is no person. Do not form the negatives of ある and いる in the same way.
Connect it to other forms
行かない means 'does not go' or 'will not go'; 行かなかった means 'did not go.' Replace the final い of ない with かった for the plain negative past. Read the time reference with the rest of the sentence.
行かないでください means 'Please do not go.' The nai-form supports several larger patterns, so distinguish a simple negative from a request or obligation expressed by what follows it.
Check: What are the basic negative forms of 買う, 来る, and ある?
Show the answer and why
They are 買わない, 来ない（こない）, and ない. Avoid 買あない, the reading きない for 来ない, and あらない as the ordinary negative of ある.