You can brush polyurethane in the same way you would brush paint. If there are any bubbles, gently brush back over the finish to burst them.
When possible, brush along the grain of the wood. Oil-based paints dry in around 8-12 hours, so they’re considerably better at leveling off and creating a smooth, brush-mark-free surface.
Most water-based paints dry in 30 minutes to an hour, which isn’t nearly enough time to completely level out. while applying water-based polyurethane you have to be extra careful.