Sand the surface of the sill using an orbital sander and 120 grit sandpaper until you remove the original finish.
Examine the wood for signs of rot. If the rot is limited to small areas near the surface, remove it with a wood chisel then patch the area with wood putty. If the rot covers a large area, or goes through the entire sill, you'll need to replace the sill.
Sand the sill with 220 grit sandpaper until it is smooth, then wipe it down with a tack cloth to remove dust from the surface.
Apply the new stain to the sill, using smooth broad strokes lengthwise over the sill. Allow the stain to dry, then add a second coat. Use an exterior-grade stain on the sill.