How To Paint Over Dark Wood Furniture?

As long as the furniture does not have a coat of polyurethane over it, then you can just go ahead and paint it using a paint made especially for wood or an all siding paint such as an acrylic.
If it has a slick shiny surface, then it has probably been sprayed with urethane. If this is the case, you will need to use a primer made for non porous surfaces before painting the wood.