Assuming you find nothing beyond problems with the finish, begin by cleaning the furniture with soapy water and a stiff brush; don’t use a power washer. Rinse and let the piece dry. Then sand with 150-grit sandpaper, followed by 220-grit. Do this by hand, going just deep enough to remove the old finish but not so deep that you take off all the bark. Wipe off all the sanding debris, ideally with something like a microfiber cloth that really grabs the dust.
Then apply a coat or two of a clear exterior wood varnish. The company suggests General Finishes Exterior 450, a clear, water-based finish with ingredients that absorb ultraviolet rays from the sun, helping to prevent damage to the wood. It comes in gloss, semigloss and satin.