[verb (dictionary form)] + な
な after a verb in the dictionary form is a blunt "don't": さわる触るな, "don't touch". It is the plain, rough way to forbid something – an order, a warning, or something said in anger.
な sounds harsh, and it only goes to someone you can order about: a friend, a child, a teammate. To ask anyone else not to do something, use 〜~ないでください, or 〜~ないで among friends.
These go beyond a bare order.
Notices and slogans use な because it is short, and there it is not rude.
A な after the ます-stem is the opposite: a short なさい, "do it". たべな食べな means "eat up"; たべる食べるな means "don't eat". The な in いいてんきいい天気だな, "nice weather, isn't it", is a different particle again; after a verb, only tone and context separate it from "don't".