Hello Bren! It depends on what the wood is; some wood have quite a high resin content. I would suggest that you sand the wood with fine sandpaper, sanding with the grain to keep it smooth, then if it seems quite dry, give the wood a thin coat of clear acrylic primer to seal the surface; ensure that you coat the wood all round and not just the surface to be painted.
Once you have a good dry surface, you could use either Acrylic or Oil Paint for your design.
Good luck and best wishes,