Use a stud finder to locate studs where you want to mount the shelf. Mark the stud locations with a pencil. Ensure they're level and spaced correctly for your brackets.

Hold the first bracket against the wall at your desired height. Use a level to ensure it's straight. Mark the screw hole positions with a pencil.

Drill pilot holes at the marked positions. If mounting into studs, use a bit slightly smaller than your screws. For drywall anchors, follow the anchor size specifications.

Secure the floating shelf brackets to the wall using appropriate screws or wall anchors. Ensure they're firmly attached and level with each other.

Sand the wood board smooth with 120-grit sandpaper. Wipe clean with a damp cloth and let dry completely before staining.

Apply wood stain following manufacturer directions. Let dry completely, then apply 2-3 coats of polyurethane, sanding lightly between coats.

Once the finish is completely dry, slide the shelf onto the mounted brackets. Ensure it sits flush against the wall and is secure.