To refinish you must brush on chemical stripper and let it sit for a while. Use a putty knife or steel wool to remove the old finish. Next sand the surface of the furniture with 220 grit sandpaper until smooth. Apply sanding sealer to the surface and let dry. Next apply a stain finish until desired coat.
To refinish a cedar chest, you must first strip and sand it but be sure to be very careful, as cedar is a soft wood and can scratch easily. After that, you simply apply the finish of your choice and let it dry.
Paint or stain? Remove the old paint or varnish. Sand til smooth. Put on new stain , wipe off, re-stain until you get the perfect color or paint over all.