Before you commit to a total make-over of that wood surface first try Liquid Gold. If further repair is needed try Murphy Oil Soap applied with a paint brush for the flat surfaces and a toothbrush for crevices and wipe with a clean dry non-abrasive cloth. Follow this with some Old English Wood Stain from the cleaner isle. If this does not work lets get started. There are 5 basic steps involved. If you wish to discover the original finish,apply denatured alcohol ( a multipurpose solvent necessary for thinning shellac). This strips shellac (a natural alcohol-soluble resin made from female lac bug secretions. The female lac bugs use this to protect their egg sacks and can be found mostly in the forests of India). If the finish is a water based polyurethane ( tough-resistant man-made resin either water or oil based) denatured alcohol will soften it but not remove it. If it is varnish( a transparent, hard, protective finish made by combining a drying oil, a resin, and a thinner) or an oil based polyurethane it will not touch it.
Use a paint brush and apply a commercial grade stripper with a brush to the dry surface and let stand at least 10 minutes but no longer than 15 minutes. Watch for the underneath surface to turn dull. Do this process outside. If it must be done inside open all windows and doors and turn fans on blowing across surface toward open windows. Inhaling stripper fumes can and has caused severe damage to lungs, heart and the brain. Be careful. Do not allow children or spectators in area. Go out and get deep breaths of fresh air every few minutes.Do not do this process if pregnant. Severe damage to the unborn child can occur.
Surface can be damp. Use a dull scraper for flat surfaces. Curves and crevices will require toothbrushes or other small devises. Be very gentle. Do not damage the wood. Do not use wire bristles.
Shellac is preferable as a sealer. It is easy to remove. Rub the surface with fine sandpaper or extra fine steel wool and denatured alcohol. Dry with a soft cloth and vacuum. Now seal using Seal Cote ( a waterproofing agent) applied with a soft cotton cloth..
When the Seal Cote is dry it is time to add color. When using stain try it on the back side or underneath for color testing. If not possible try it on a similar piece of wood. Maple, cherry and pine will not absorb stain evenly & should be dyed and not stained .If a glaze is used putting coats on top of each other without drying in between causes smearing. Let one coat dry and then cover with a coat of spar varnish (An oil base blend of natural oils and synthetic resins) between each coat of glaze. Be sure surface is dry before applying next coat of anything except stain. Spar varnish should dry overnight or as directed on container.
When surface is dry apply 2 coats of gloss varnish drying between coats and then finish off with a coat of satin spar varnish.
Pandolft, Keith, Woodwork Refresher Course, This Old House, March 2009, Pg 37-39