能 can indicate something that you are able to do naturally, for example:
I can eat 3 bowls of cooked rice.
Wǒ néng chī sān wǎn mǐfàn.
能 can also be used to ask for or give permission, for example:
Can I smoke here?
Wǒ néng zài zhèlǐ chōuyān ma?
No, you can’t.
会 means that you have acquired certain abilities or skills, and that you have acquired them through learning, for example:
I can speak Mandarin.
Wǒ huì shuō pǔtōnghuà.
I can cook.
Wǒ huì zuò fàn.
Can you drive?
Nǐ huì kāichē ma?
“会” also indicates what might happen in the future. For example:
It won’t rain tomorrow.
Míngtiān bú huì xià yǔ.
Welcome to have my 1-ON-1 lessons on http://www.verbling.com/teachers/dawei 🙂