The first step to finishing a piece of furniture with varnish is preparing it with sanding. Your final results will only ever be as good as the work that went into achieving them. Don’t cut corners when it comes to sanding, as any scratches or damage will become even more visible once your coating is applied. Step right up through to 240-grit before coating with varnish. If you feel any roughness to your varnish coat after it has dried, lightly sand it down with 240grit before applying the next coat. - MitchellMc
Brushing too much not only creates more air bubbles but also makes the solvent evaporate. The bubbles will not have enough time to pop and brush marks will not have enough time to flow out. - Kermit
I've had issues getting a good finish in the past, especially when using brushes on the more "affordable" end of the scale. When using some of the cheap and nasty throw-away brushes, the finish could always be nicer.
These days when I plan out any painting job, I now realise that I should expect to be spending at least $25-$30 on a good quality brush. However with this sort of equipment, if it is cleaned properly after each use there's no reason you cannot hang onto these for a couple of years. Unfortunately the old 5-pack of brushes for $5 special will never give you your desired result.
If you are in a situation where you have a decent quality brush and still find brush marks or bubbles, there is a technique called feathering, an easy process where once you have good coverage of your varnish on the surface, very lightly drag the tips of the brush bristles across the varnish, in the same direction first applied, and this will give a nice even finish. - Simon