You can buy wood dowels in common species like walnut, cherry, and pine, but if you need a dowel in an uncommon species, or if you're making authentic reproductions, or you just like to try different techniques, here are three ways to make them.
One: Use a beading plane to round over both sides of a board, then snap off the dowel. Shave the rough, snapped-off edge with a block plane or chisel. Match the thickness of wood with the diameter of the bead so the dowel is perfectly round.
Two: Use a block plane to round over a square blank and eyeball it as you go. This works great if you like that imperfect, handmade look, like you find in PA German furniture. (If you take your time, though, you can make very precise dowels with this technique.)
Three: Use a dowel plate (mine is from Lie-Nielsen). Make sure you cut your blank very close in size to the final dowel diameter, otherwise, it's likely to split as you tap it through. Use a chisel to taper the leading end. Dowel plates work best with short pieces of wood.