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.

It doesn't really matter anyway. In one thousand years English will have changed entirely and our arguments about 21st century grammar will look ridiculous.