To carve a star, follow the basic principles in lettercarving. For this technique, you only need a straight chisel and a mallet (not even a mallet, if you push hard enough to make your stop cuts). And you'll make life easier on yourself if you create a star where any two points share a common wall—a straight line drawn from point to point. 
In the illustration above, the dashed lines are low spots, the valleys, where you will make the stop cuts.
This star is 1.875" diameter, so I'm using a 20mm straight chisel: small enough to manage but large enough that the width of the blade is wider than the deepest cut and almost as wide as the stop cut is long.
First, define the stop cuts. They should not be deep as the final depth of cut and should taper to nothing at the star's points. Bevel up, start at any point and ease the chisel into the cut, gradually slicing deeper as you reach center, then easing up again as you approach the opposite point. Here is the advantage of two points sharing a common wall: with one cut, you have established one of the two walls on each of two spurs of the star.
Keep an eye on the grain direction to avoid tearout and work your way aroun
d the star. You should not try to remove the waste in one slice, but ideally two (I've never mastered this). With subsequent passes, be sure to lay the chisel's back flat against the wall created in the first slice to ensure a clean, single facet, wall.
Remove stubborn pieces by continuing the slicing method and/or by sliding the chisel directly downward into the valleys.
In the photo at right, you can see tearout on the upper right spur. Slicing with the grain is most difficult and tearout means you should cut in the other direction. I cleaned it up fairly well with very light paring slices. Not perfect, but no one will inspect your work
as closely as you (or another woodworker!) will.If the spurs do not meet in the middle, that means the walls' angles are not consistent and you'll have to carefully pare the shallower walls to match the sharpest-angled walls.
I'ts easier than you might think to carve a star, but it's a design element that prompts admirers to say "nifty!"