"No, we do not cook."
Translation:Нет, мы не готовим.
Готовит - 3rd person. Готовим - 1st persom.
«нет» is a contraction of «не есть» meaning "there is not" but it is also used to mean "no" when on its own. So you'd see «нет» in places you'd otherwise see «есть» when the statement is negative.
(It's not quite true historically that it's short for «не есть» as it really came from older words «не е ту» which are no longer in use, but the meaning is the same so no harm no foul.)