The short answer is 1-2 times per week, however it really depends on the breed, and type of hair your pup has.
The main purpose of brushing out your dog in between groomer visits is to ensure that they don't form any matting, or tangles in their hair, and to help cut down on the amount they shed. When a dog gets matted sometimes the only way to fix it is to give your dog a really short hair cut, which may not be the cutest. Brushing your dog also helps to keep their hair healthy, clean, and ensure that your pup doesn't have any tick bites, scratches or other things that may need to be looked at by a vet.
Short and Smooth hair- like Dobermans or Pugs only need to be brushed out once a week.
Short and Wiry or Short and Double Coated hair - like Schnauzers, or Labrador Retrievers need to be brushed out twice a week.
Long or Curly or Double Coated hair- like Maltese, Poodles, or Golden Retrievers should be brushed 3-4 times per week.
Brushing out your dog is an important practice to keep your dog looking good, and can be a great way to bond with your pet! Make sure to give lots of belly rubs or treats for good behavior during brushing!