見るな - Don't look. - quite strong way of asking not to look at a specific thing, and sounds rough and manly For example. You are writing your secret diary, and someone is trying to look at it, then you would say - 見るな ーit sounds so much like a man, so only use if you are a man. 見ない - I don't look. - this is not asking, just saying you don't look at something generally. ー I don't watch TV. 私はテレビを見ない。 見ないで - Please don't look. This is softer way of saying not to look at something specific. You can use in same situation as 見るな I hope it helps!

Aki's answer is good. But we also use the both of 見るな and 見ない as "Don't look at/see/watch". （When a parent order his/her child not to watch TV） Father: テレビは　宿題<しゅくだい>が　終<お>わるまで　見<み>るな！／テレビは　宿題が　終わるまで　見ない！／テレビは　宿題が　終わるまで　見ちゃ　ダメだ。 Don't watch TV until you've finished your homework. Mother: テレビは　宿題が　終わるまで　見ない！／テレビは　宿題が　終わるまで　見ちゃ　ダメ。 Don't watch TV until you've finished your homework. If you say テレビは　宿題が　終わるまで　見ないで。, it sounds like a wish. You can also use dictionary form and te-form as an order/command. わからなかったら、さっさと　辞書<じしょ>を　見る／見て！ If you do not know it, look at quickly dictionary! 　　　strong　　　　　　→　　　　　 　　　weak 見ろ／見るな＞見る／見ない＞見て／見ないで