Better Brushes are the Key
Usually, a brush is the best tool for applying polyurethane. For water-based poly, a synthetic brush (such as nylon or polyester) is best. For oil-based poly, use a natural-bristle brush. In either case, plan to spend more for a good-quality brush. Quality brushes hold more finish, lay it on smoothly and are less likely to leave lost bristles in your clear coat. If you clean your brush immediately after use, it'll serve you well far into the future.
Leave Mistakes Alone (Usually)
When you notice a run, missed spot or other problem in the polyurethane you applied minutes earlier, you'll be tempted to brush it out. Don't. The finish may look wet, but chances are it's already sticky, and brushing will only make a mess. There are a couple of exceptions to this rule: You can pop tiny air bubbles with a pin, and you can pluck out a hair, a lost bristle or unfortunate fly using sharp tweezers and a steady hand.