Place the shutters in a well-ventilated work area, or outdoors.
Sand the shutters, including their sides, gently with a fine-grit sanding block to remove snags, splinters and rough spots. Wipe dust away with a tack cloth or soft brush.
Move the shutters and cover the work surface with newspaper. Set the shutters atop the newspapers.
Wet the bristles of a wide paintbrush with water. Brush a light coat of water over all surfaces of the shutters to help the stain soak in evenly.
Open and stir the stain to ensure all particles are thoroughly mixed in. Put on rubber gloves to protect your hands, then dip part of a folded rag into the stain.
Rub the stain over the entire top and sides of the shutters, working in the direction of the wood grain. Use a narrow paintbrush to get in between louvers.
Allow stain to set for a few minutes or as directed by the stain manufacturer's instruction. Rub off excess stain with a clean rag.
Flip the shutters over and stain the back side by rubbing the stain on with a rag, allowing it to set for several minutes, then wiping off the excess with a clean rag. Check the front side to make sure no stain dripped through; if it did, wipe it off. Allow to dry completely.
Open and stir the varnish or polyurethane with a stir stick. Apply a coat of the sealer onto the shutters with a paintbrush, wiping up drips with the brush as they occur. Allow the sealer to dry as recommended by the manufacturer, then flip the shutters over and seal the other side, allowing it to dry as well.
Sand all sealed surfaces gently with a fine-grit sandpaper to create a smooth topcoat. Do not sand hard enough to remove any of the sealer. Wipe with a tack cloth to remove dust.
Repeat Step 9 for a second coat of sealer for added shutter protection.