I can't do it/I'm not able to do it means the same, but in some cases it suggest different opinions. Example, if a teacher told a student; I can't teach you, it suggest that the student is too stupid or not willing to learn I'm not able to teach you, it suggest something/someone else is to blame. I don't know means that you don't have the knowledge to do so, same example; I don't know how to teach you, because I'm not a teacher;-)

I can't do it - "Je ne peux pas le faire." Le plus général de les trois phrases. ("Je ne pas le temps ou la capacité". "Je ne sais pas comment le faire." Mais aussi, "Je manque quelque chose et je n’ai pas le contrôler.") [The most general of the three sentences. ("I don’t have the time or the capability", "I don’t know how to do it". But also, "I’m missing/lacking something and I don’t have control over it.")] I'm not able to do it - "Je ne suis pas capable de faire ça" ou "Je ne peux pas le faire" aussi, mais à cause de moi seulement. ("Je ne pas le temps ou la capacité". "Je ne sais pas comment le faire.") ["I don’t have the capability to do it", or "I can’t do it" also, but only because of me. ("I don’t have the time or the capability", "I don’t know how to do it.") I don't know how to do it? - "Je ne sais pas comment le faire." (même si j'ai le temps pour le faire, par exemple.) ["I don’t know how to do it" (even if I have the time to do it, for example.]

It would easier to explain if you have the phrases in context.. do you have full sentences you're not sure about which to you it in? Otherwise, Anders has just about the best explanation out there.

Hello! Well, here we go: "I don't know how to do it" refers to the impossibility of doing something IN A CERTAIN WAY (due to lack of knowledge or something else). "I can't / I'm not be able to" refers to the impossibility of doing something BECAUSE OF PROHIBITION for example. I hope this helps you. Greetings man!