Deck staining is exterior painting's close cousin, and the same rule holds: most of the job is what happens before the stain comes out.
The wood gets cleaned first. Dirt, pollen and that gray film on weathered boards all keep stain from soaking in, and anything left sitting on the surface is what peels later. Then it has to dry all the way through, which in a Tennessee summer is not the same afternoon. Raised nails get set, rough spots get knocked down, and only then does stain go on. Floor boards, rail caps and every baluster, brushed into the gaps so the sides of the boards are covered and not just the tops.
The roof is a real advantage on this one. It keeps most of the sun and rain off the floor, so the stain here will outlast the same job on an open deck in full sun. The open side still takes weather, and that is the part to keep an eye on.
We also hung new curtains along the covered end. Small thing, but they are a lot of why the deck feels like an outdoor room now and not a platform.