The application of polyurethane to wood is quite easy, and there are multiple methods. The most common method is to brush it on with a paintbrush. If you go this route, I would recommend a soft foam brush, as it is less likely to leave streaks and other unsightly marks. I would also urge you to make sure that you wait for the recommended amount of time between coats. Otherwise, your bottom coats will never fully dry and may remain cloudy.
If you want to make things easier, you can just get a can of spray-on polyurethane. This tends to be a little more expensive, but its an ideal choice for small tasks. You can just hang the item from a wire and give the whole thing a nice, even spray. Of course, you do have to make sure that you spray evenly to avoid leaving unsightly globs and drips of excess plastic.
Whatever method you choose, the application of a polyurethane layer should always be the last thing you do to the table. This polyurethane top-coat provides the first line of defense against damage, so you don’t have much choice there.