Learn Turkish: Biz on bir öğrenciyiz.

It is very straightforward! You just combine the word for ten (on) and the word for one (bir) with a space between them. So, on bir literally means 'ten one'. This pattern works for all numbers from 11 to 19.

Why isn't it öğrenciler since there is more than one student?

In Turkish, whenever you use a number before a noun, the noun stays in its singular form. Since we already specified the quantity with on bir, adding the plural ending to öğrenci is considered grammatically incorrect.

What does the -yiz at the end of öğrenciyiz do?

It acts as the 'we are' part of the sentence. In Turkish, 'to be' is often a suffix attached directly to a noun or adjective. The base suffix for 'we' is -iz, but because öğrenci ends in a vowel, we insert the buffer letter y to connect them smoothly, resulting in öğrenciyiz.

Is it strictly necessary to include Biz at the beginning?

No, it is optional. Because the ending -yiz on öğrenciyiz already tells us the subject is 'we', you could just say On bir öğrenciyiz and the meaning remains exactly the same. Biz is used here simply to add a little emphasis.