What does a negative prefix do to a word?
Adding a negative prefix to a word produces a new word that expresses a kind of oppositeness to the original base. There are five prefixes that can do that; here they are with some adjectival examples:

a- ... moral (concerned with the principles of right and wrong behaviour) ~ amoral (lacking morals, unconcerned with those principles).

dis- ... loyal (firm and constant in one's support for someone or something) ~ disloyal (lacking loyalty or support...)

in- ... secure (certain to remain safe and unthreatened; fixed or fastened). ~ insecure (uncertain or anxious; not firmly fixed).

non- ... violent (someone who uses physical force to hurt damage or kill someone or something). ~ non-violent (someone who uses peaceful means to achieve their objectives).

un- ... tidy (arranged neatly and in order). ~ untidy (not arranged tidily).

All those examples and definitions came from my Oxford Dictionary; it wasn't difficult. Why don't you try the same exercise using other words like (a)typical, (a)political, (dis)courteous, (dis)honest, (in)discreet, (in)tangible, (non-)essential, (non-)standard, (un)common, (un)just. Some simple spade-work and you'll soon get the idea behind negation prefixes.

It makes the opposite of a word.
Try out our live chat room.
They form the opposites of the words. (Hint: The name itself says: negative)
Here are some examples and usages:
http://www.linglish.net/2008/09/15/so-many-negative-prefixes /

 BillJ's reply was promoted to an answer.