There are a few ways to fix a loose wooden stair railing. The most common way is to use wood screws and glue. You can also use nails or metal brackets. If the railing is really loose, you may need to remove it and replace the screws or nails with longer ones. Make sure that the new screws or nails are long enough to go through the rail and into the wall or floorboard behind it.

If the railing is loose because the screws that hold it in place are stripped, then you can use a power drill with a Phillips head screwdriver bit to re-attach the railing. If the screws are too tight and impossible to remove, then you'll need to cut them off with a hacksaw. If the railing is loose because it's been warped by moisture, then you can try straightening it out by applying heat from a hair dryer. If that doesn't work, then you can try attaching it in place with wood glue or construction adhesive.