Where is the move tutor in Pokemon black?

You're likely thinking of the Move Relearner in Pokemon Black. There is no "Move Tutor" in Pokemon Black.

The Move Relearner is located in Castelia City inside the Pokémon Center. You can find it on the second floor, past the Nurse Joy's desk.

The Move Relearner allows you to teach your Pokemon moves they have previously learned. You'll need to use Heart Scales to do this.