The obvious solution to avoiding brush marks while painting furniture is not to use a brush at all, but to use spray paint instead. However, spray paint poses its own difficulties, such as a tendency to drip and coat unevenly. If you are committed to using a paintbrush, you can avoid brush marks by using some specific techniques. Practice on a piece of scrap lumber before you try painting your furniture.
Sand the wood with an orbital sander to achieve the smoothest surface possible. If the wood has been previously painted, look for ridges, drips and divots that require extra attention. Use a pull scraper for ridges and fill depressions with spackle prior to sanding.
Wipe the sanded surface with a wet cloth to clean off sanding dust. Let the surface dry completely.
Add a flow extender to your paint, if possible. This reduces the surface tension of the paint and helps it distribute more evenly, smoothing out visible brush strokes.
Use a professional-grade paintbrush matched to the type of paint you're using -- china-bristle brush for oil-based paint and a polyester brush for latex-based paint. A high-quality paintbrush yields a better result than an inexpensive or disposable brush.
Apply the paint with the wood grain, using long, smooth strokes, working on one section at a time. As soon as the surface is painted, knock the remaining paint off the brush into the paint can or tray. Immediately tip off the painted section by holding the brush at a low angle and lightly running the bristles over the painted surface, evening out visible brush marks.
Leave the surface undisturbed until it is completely dry. Once the paint begins to dry, any further brushwork will leave visible marks.