The key to finding the difference is to look at the character after 不 and more importantly, to look at the rest of the sentence. 不 - no/don't 我不喜欢喝茶 = I don't like tea. 你想去吗？不想。= Do you want to go?No. 不是 - is not, am not：他不是中国人= He is not Chinese. 我不是说...I'm not saying.... 不用 - Don't, No need：你不用找了- You needn't look for it. 不用担心= Don't worry 不要 - Will not- do not - must not- don't want will not：不要害怕 =don't be afraid，我不要去上课-= I don't want to go to class/I wont go to class. 不要忘记我爱你 = Don't forget I love you 不能 - Cannot/not able/should not: 这件事做了一半，你不能甩手不管=You're only halfway through. You can't wash your hands of the matter now.你不能把这间房出顶，房主会不高兴的。 You can't re-rent this room to someone else, the owner of the home wouldn't be happy. 不行 - No, Not okay, be forbidden, won't work/be of no use: 你这个办法保准不行 = Your method is destined to fail. 我们去星巴克，行不行？不行=We'll go to Starbucks, okay? No! 不可以 - Cannot/cant/not allowed, not okay 不会- Cant-will not....... I'm not going to write examples for those last two, as I hope you now see the difference is in the word after, and all can be used and translated in different ways!

So... it's a little weird. 要 means "want" (among other things), but 不要 means "Don't!" If you want to say "you don't have to" you say 不用. 可以 is about having permission or it being okay to do something. So 不可以 is "can't" in the sense if "it's not permitted" or "it's not okay to do that". 会 has the meaning of "to be likely to happen" many times, so 不会 means "it's not likely to happen". BUT 不会 is casually used as a response to 谢谢 -- just accept it, don't overanalyze it. ;-)

不 = no 不是 = isn't 不用 = no use 不要 = won't 不能 = can't 不行 = not allowed 不可以 = isn't able 不会 = isn't taught / isn't possible