A tripod will help if you are using slow shutter speeds, becaue there will be less risk of camera shake, but won't prevent blur with a moving target.
If you're using f4 with quite a long lens you'll find depth of field is very limited so try and focus on the most important area, which in the case of dogs etc, is usually the head and eyes. Using a smaller aperture (higher f number) will give you a better focus range, but will mean that you have to use an even slower shutter speed to compensate for the lens letting less light reach the sensor...
You can't win, so bang the ISO up to what you