Your forearm muscles are an endurance muscle and a very stubborn muscle to get to grow. It would be the equivalent of trying to get the muscles in your jaw to grow. I would train them 3 days per week or every other day.
The nice thing about forearms is that you can train them really easily at your desk at work or at home.
Hand grippers are a very effective exercise to develop the forearm muscles. You can put a set for cheap on amazon.com.
In addition, I would also start doing wrist curls and reverse wrist curls to fully train your forearms. You can easily pick up some 15 pound dumbbells for cheap at a local fitness store to do wrist curls at your desk at work.
I would do 4 sets of each each exercise, 8-12 reps per set, 3-4 days per week. If you want to do them at work, MWF would be optimal.