Particle board is made out of wood particles and resin pressed together into sheets. It's often used for inexpensive furniture and shelving. Particle board furniture is always coated in veneer, which is somewhat durable but still prone to scratching. It cannot be sanded smooth because the wood doesn't have a grain, so fixing it involves filling in the scratches and replicating the finish. Once repaired, a coat of sealant protects the finish from further damage.
Spray a rag with furniture polish and clean the area to be repaired. Allow to dry fully.
Apply a bit of wood filler to the scratches with your finger. Smooth the filler with your finger and wipe the excess wood filler away with a very slightly damp rag. Skip this step if the scratches are not deep enough to require filler. Allow to dry fully according to package directions.
Color over the scratches with a varnish marker in the appropriate color stain. Allow to dry according to package directions. Repeat the process until the scratches match the surrounding wood.
Rub a wax pencil across the scratches. Buff the wax with a lambswool buffing pad until all excess has been removed.
Take the piece to a well-ventilated area. Put on a face mask and spritz the wood lightly with clear spray lacquer according to package directions. Repeat as necessary to produce the desired sheen.