Use medium-grade sandpaper on the surface of the maple cabinets to smooth out rough areas. You should be able to run your hand over the surface of the wood without it resisting your fingers or creating splinters. Then use the fine-grade sandpaper to go over the wood again to create an even smoother surface in preparation of staining and finishing.
Wipe the surface off the sanded maple wood with a clean, dry cloth to remove dust and dirt before staining. Go over the wood several times with a clean, damp cloth to make sure that nothing will be caught in the stain or finish on the wood.
Lay out a plastic tarp to protect the area where you will be staining and finishing, and cover your hands with plastic gloves. Test your cherry stain on a scrap of maple wood and allow the stain to dry to see how the color will take to the wood before you begin staining your cabinets.
Apply the oil-based cherry wood stain with a large, stiff paintbrush. Go over the surface of the cabinet with smooth strokes of stain and make sure that you cover the surface of the cabinet evenly. Let the stain set for 15 minutes to see how the color takes. Add one or two more coats of stain, depending on how dark you want the cherry stain to appear on the maple wood. Allow the cherry stain to dry for at least four hours between coats.
Finish your cherry-stained maple wood with a semi-gloss polyurethane wood finish to give it an even richer color and a glossy shine. Remove dust from the surface of the stained, dry wood with a dry cloth, and make sure you are set up to work on the plastic tarp and in a well-ventilated area. Stir a semi-gloss finish with a wood stick and wear plastic gloves before you add the finish to the wood.
Use a clean, stiff paintbrush to apply the finish on the surface of the cherry-stained wood in an even coat with paintbrush-wide strokes. Allow six to eight hours for the first coat to dry. Apply two even coats and let the stained and finished wood to dry. Allow at least 12 hours for the surface off the maple wood cabinets to dry completely.