The use of adverbs in english

I just realized that I need to get help with understanding how to use adverbs in English. Let's say that a guy is nice, and he performs every action in that way.

Does he:
a) act nice
b) act nicely

Which one is the correct one and why is it so? Don't be afraid to use grammatical terms.

>>5
Yeah, I know. There's technically no "standard" rules of English (besides what's agreed upon by English teachers and the like who write all the grammar books). We have no equivalent of the Academie Français.
Which is good, it lets the language evolve. I personally like Southern English, ain't and y'all are pretty convenient. Except of course in obvious situations like job interviews where you want to talk in very educated speech. And outside of the south, people will look at you like an idiot for using them...

>>6
This. It probably won't change as much as it has in the past 1000 years, but no doubt it'll be simplified as hell (god forbid we use something similar to ebonics)