A small bead of silicone adhesive caulk(color matched preferred) along the top, and maybe 3-4 dabs on the back of the backsplash. Install the backsplash pushing into the wet caulk. Clean up any squish out. I usually run a small bead along the top/spalsh joint for looks, smooth with my finger. A bead at the top of the splash, but not with silicone, paint will not stick to it.