A question was asked on QuiltArt about dyeing wood. I dug out the wooden stars I dyed about 4 years ago.
This is a fairly vague description of what I did. (It has been a while & I was experimenting.) I used a plastic cup. Fill cup about half full of soda ash, put in wooden stars. Set aside to soak for about 30 minutes. Poured off most of the soda ash solution. Added dye to enough water to fill the cup about half way - covering the stars, poured it into the cup, making sure stars were covered. Covered the cup with plastic wrap. Left sitting until the next day.
They took color well. Where one star was lying on top of another, the dye was partially blocked, which you can see in the picture. The white flecks are bits of fluff from sitting around for all this time! If I were to do it again, I would make sure to have a single layer of wood objects.