Are you a teacher?

Remember the word 'teacher' is a common noun, and the general rule of thumb is that before a common noun, you will need to add an article such as a, an or the (or demonstrative pronoun such as that, this etc) :)

Are you a teacher?

You should distinguish between countable nouns/可数名词 and uncountable nouns/不可数名词. As 'teacher' is a countable noun, you have to put 'a' before it. As for whether you should put an 'a' or an 'an', just see the first syllabe/音节 (not the first letter) of the following noun.

For example,

'an egg', The first syllable is /e/, so you use 'an'. 'an umbrella', its first syllable is /^/, a vowel/元音, so you also should put an 'an' before it. 

'a teacher', its first syllable is /t/, a consonant/辅音, so you use an 'a'.

Just some grammar question...

Are you a teacher or Are you teacher?

"Are you a teacher?"  is correct.

I'm happy to help you more!  --- Colt