How many times per week should I get my child to take lessons?

The norm among many parents is to do this once a week, but in my opinion, once a week is not enough and past the initial phase of your child’s getting some exposure to the instrument, twice a week will make the progress a lot better.
 
Later on if your child advances and plays really mature pieces and concerti, you will see that even twice is week is not enough to cover everything, since one movement of one concerto can take 20 minutes, and after a couple of repetitions and corrections, the one-hour time limit is over.