Power wash and apply new finish after table is dry.

I'd lightly sand off any splintery bits, then use a semi-transparent "driftwood" stain.

If you have a power washer, use that. Otherwise a jug of deck cleaner from the home center (follow the directions). Let the table dry for a few days up to a week depending on local weather conditions. Then a nice sanding to smooth things out and remove the "splintery bits." Then top coat with either a semi-transparent or opaque stain depending on the look you're going for.

If there is no prior stain you can get a wash with oxalic acid in it (the more the better or better straight oxalic acid.

Let it sit a while on the surface and do it's thing...keep it wet. This will brighten the wood.

Then rinse off. Be careful with a power washer, you can damage the wood. Lower psi and higher gpm (gallons per minute) is best. Start with the wand far from the surface and work your way closer. Then let dry and sand, the water will raise the grain.

If there is stain you'll need to strip it off first. Use potassium or sodium hydroxide. Do this before the oxalic wash. Mixed chemical light strength first you can always make it stronger. Power wash as said above. Then wash with oxaclic right away. If on grass keep the grass wet or it will be brown. I would do this in light rain, if on grass.

Always use personal protection equipment.

Sorry, didn't see the part about not wanting to strip the previous coating. So just wash, sand stain. Just match stain type, water base or oil. You'll probably want to wash and recoat horizontal surfaces every year to keep it looking good. Vertical surfaces could go about 3 years before recoating

http://www.familyhandyman.com/decks/deck-rescue-renew-your-deck/view-all