Learn Spanish (Latin America): Yo no soy el profesor.

In Spanish, to make a sentence negative, you simply put no directly before the conjugated verb. While English puts 'not' after the verb in 'I am not', Spanish says Yo no soy (literally 'I not am').

Do I always have to use the word yo (I) in this sentence?

No, you can just say No soy el profesor. Because the verb soy is only ever used for 'I', the yo is optional. Including it just adds a little emphasis, like saying 'I am not the teacher.'

Why is it el profesor instead of just profesor?

You use el here because you are talking about the specific teacher. If you just wanted to state your profession in general ('I am not a teacher'), you would drop the article and say Yo no soy profesor.

How would this sentence change if a woman is speaking?

If a woman is speaking, both the article and the noun change to match her gender. She would say Yo no soy la profesora.