What is the best way to vent a dryer?
Based on your description, I will assume that the existing vent is a short run, on a straight line, into the garage. What you want to do is remove the vent hood from the interior garage wall, install an elbow, and run the vent to the outside of the nearest garage wall. Reinstall the hood to the outside wall and you will be in good shape. Also, inspect the vent hood to make sure that the flap is working properly, if, in fact, it is even there. If not, get a new one. This is very important because it will not only prevent cold air from getting into your home, but will also keep “critters” and insects from entering your house via the laundry room. Believe me, it will happen. Whatever you need to reroute the dryer vent should be available at your local hardware store.