Learn Turkish: Merhaba! Sen öğretmen misin?

In English, we say "Are you a teacher?" but in Turkish, when stating or asking about someone's profession, you usually drop the word bir (a/an). You just literally ask "Are you teacher?".

What exactly is misin made of?

It is made of two parts: mi is the yes/no question particle, and -sin is the personal suffix for "you" (sen). When asking a "yes/no" question about "you", the personal suffix attaches directly to the question particle, not the noun. Note that the question particle is always written as a separate word from the noun before it!

Why is it spelled misin with an "i" instead of mısın or musun?

This is due to 4-way vowel harmony. The question particle always matches the last vowel of the word right before it. The last vowel in öğretmen is "e". According to vowel harmony rules, an "e" is followed by an "i", making the particle mi. The -sin ending just matches that "i".

Could I leave out the word sen at the beginning?

Yes, you can! Because the ending -sin on misin already tells us exactly who you are asking ("you"), the word sen is optional. Saying just Merhaba! Öğretmen misin? is perfectly natural and very common in everyday Turkish.