Learn Finnish: Hei! Minä olen opettaja.

Finnish doesn't have articles like 'a', 'an', or 'the'. The word opettaja simply means 'teacher', but it translates to 'a teacher' or 'the teacher' in English depending on the context of the conversation.

Could I just say 'Olen opettaja' without the word minä?

Yes! In Finnish, the ending of the verb (the -n in olen) already tells us that 'I' am the one doing the action. Because of this, it is very common to drop the pronoun minä completely.

Is this exactly how Finnish people would say this in casual conversation?

This sentence is in standard or written Finnish. In everyday spoken Finnish, people usually shorten the words and say mä oon opettaja instead of minä olen opettaja.