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Ensure that the floating shelf will fit the cleat precisely, hold the shelf up to the cleat as well as do a dry fit one that doesn't entail adhesive or screws. Make any type of modifications to fit as necessary. When you are specific the fit is precise, apply wood glue to the top of the cleat, and afterwards fit the shelf over it. Safeguard the shelf to the cleat using brads nailed in from the top of the shelf down right into the cleat.