ない形
nai-kei
Draw one X. Everything else stands on it.
The picture You draw a single X on the spot where the action would have gone. All that changes is what you then say about that X. てください asks you to fill the slot; ないでください asks you to leave the X where it is.
Where the picture shows up in ない形
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just the X
今日は残業しない。
kyō wa zangyō shinai
I'm not working overtime today.
Today's 'overtime' slot has a single X drawn across it and is left that way.
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keep the X there
お酒は飲まないでください。
osake wa nomanaide kudasai
Please don't drink alcohol.
A palm covers the X drawn over the glass, keeping anyone from rubbing it out.
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the X as your goal
遅刻しないように、早く出ます。
chikoku shinai yō ni, hayaku demasu
I leave early so I won't be late.
An arrow is aimed at the X on the 'late' slot, and you leave the house early to keep it there.
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the X is fine too
明日は来なくてもいいです。
ashita wa konakute mo ii desu
You don't have to come tomorrow.
You glance at the X sitting in tomorrow's box, shrug, and walk on — it can stay.
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the X is not allowed
パスポートを見せなければなりません。
pasupōto o misenakereba narimasen
You must show your passport.
A red line is struck through the X in the passport box: while the X is there, you don't get through.
Literally 'if you don't show it, it won't do.' Two X's stacked make an obligation.
All of it in one picture
ない is not the word 'no'; it is an X drawn on the slot where the action would have gone. Leave the X alone and you have a plain negative; guard it with your palm and you have a prohibition. Aim at the X and it becomes 'so that it won't happen'; shrug at it and it becomes 'you don't have to'. Refuse to let the X stand and it becomes 'you must'. One X — and five different attitudes taken in front of it.