To polish leather boots, start by removing any dirt or dust with a soft brush or damp cloth. Once clean, apply a small amount of leather conditioner to keep the leather supple and prevent it from drying out. Allow the conditioner to absorb for a few minutes. Next, choose a high-quality shoe polish that matches the color of your boots. Using a soft cloth or applicator brush, apply the polish in small, circular motions, covering the entire surface of the boots. Allow the polish to dry for a few minutes before buffing the boots with a clean, dry cloth to achieve a glossy shine. Repeat the process as needed to maintain the boots and keep them looking sharp.