Thumbs up to Rose, who wrote a good, concise answer while a was preparing this more detailed one.
Grammar:
I’d recommend less redundancy — in English, there is no need to say that you are a “teacher who teaches.” It’s also not necessary to mention that you teach “students” — anyone you teach is your student by definition. If there’s anything special about your students (like their age), then feel free to mention it.
If you mention “students,” then we need to use the infinitive, not the gerund.
I don’t know that much Chinese, but your expression would appear to correlate more with the English word “handicrafts” rather than fine art. I’ve copied the definition below. (You could also say “arts and crafts,” as Rose suggests. The difference is subtle — “arts and crafts” sounds more like recreation, whereas “handicrafts” is more general, including also commercial activity. Assuming your students are young, the more specific “arts and crafts” may well be a better fit.
I would actually say something like “I teach handicrafts” or “I’m a handicrafts teacher.”
From the Oxford on-line dictionary (UK, but applies equally to American English):
handicraft
Pronunciation: /ˈhandɪkrɑːft/
NOUN
[MASS NOUN] (also handicrafts)
1Activity involving the making of decorative domestic or other objects by hand:
the traditional handicrafts of this region
Source:
http://www.oxforddictionaries.com/definition/english/handicraft?q=handicrafts
Also, the Wikipedia uses the term “handicrafts” as the main term:
https://en.wikipedia.org/wiki/Handicraft