Sand the scratches one at a time on the desk surface, starting with a medium-grit grade of sandpaper. Work the paper in the direction of the wood grain as much as possible. Press lightly to work out the scratches, because sanding too hard may create a rut in your work surface. You can always sand off more wood by working gently.
Switch to progressively finer-grit sandpaper as each scratch begins to fade.
Wipe the desk surface with a damp cloth to remove wood dust. Wait for the desk top to dry completely.
Apply wood stain to match your desk finish in long, even strokes over the sanded area. Work the stain in the same direction as the wood grain for a smooth finish.