i am no artist is not correct translation, should be i am not artist (what actually was wrong for me) or the conjunction i'm not
I don't quite know what you're asking ... but these are correct sentences in English with almost the same meaning:
I am not an artist. (This is a normal sentence but pronounced very clearly, or stressed.)
I'm not an artist. (This is a normal sentence with normal pronunciation.)
I am no artist. (This sounds defensive.)
I'm no artist. (This sounds defensive.)
You cannot just say "not artist". We need an article in English: an.
This is the neutral word order. "Nem művész vagyok" means that "I'm not an ARTIST (implied: but something else)"
Does anybody know when it is okay to drop the article, as in this sentence?
In case your question refers to the Hungarian version of the sentence, the answer is that you can drop the indefinite article 'egy' any time.
Is there a reason it's not: "Nem művész vagyok" instead? I seem to recall that to say "I am an artist," you would say "művész vagyok". Is this wrong?
No particular reason - this is just another sentence with a slightly different meaning. 'Nem művész vagyok.' says it's not an artist what I am (but I am something else nevertheless). 'Nem vagyok művész.' says I'm not [certainly] an artist (and no further hint is given if I am something else at all).