Move items out of the cabinets and off of cabinet surfaces. Cover the floor and appliances with plastic drop clothes so dust and paint don't get on them.
Remove the cabinet doors, and take off the hardware.
Sand the surface of the cabinets and doors with 100-grit silicone-carbide sandpaper to remove the finish and any other residue. The wood finish is slick and prevents the paint from bonding to the wood well. Make sure to get in all of the corners.
Wipe off the cabinets with a damp rag or sponge when you are done sanding, and allow them to dry.
Fill in holes or dings with wood putty.
Tape off the edges around the cabinets that won't be painted. Use blue painters tape. This will prevent some accidental drips on walls or tile.
Paint the cabinets and doors with a solid coat of brushing putty, which is a type of oil-based primer that fills in wood grains well. This is best for oak cabinets that have a deeper wood grain that can show through paint. Use a bristle paintbrush and paint in an up-and-down direction when possible.
Sand the primed surface with 220-grit silicone-carbide sandpaper to smooth it out.
Paint cabinets and doors with an oil-based paint in the color of your choice. Use a bristled brush in up-and-down strokes when possible.
Sand when dry with a 280-grit silicone-carbide sandpaper.
Apply a second coat of paint, and allow it to dry. Sand and apply a third coat if needed, in the same manner. If a third coat is not needed, then just allow to dry.