If you've got a copper sink, you're going to be pleasantly surprised by how low maintenance [1] it is. All you need to do is wipe it down with a mild dish soap and water a couple times per week. Use a cloth or sponge to wipe away the grime. Never scrub it with steel wool or abrasive cleaning tools; it will leave harsh scratches. Make sure to dry it down after cleaning [2] to avoid creating any water spots on the copper finish.
You will also keep your sink looking great if you avoid letting any acidic foods sit on the surface. The acid will eat away at the copper and leave a discolored finish. Think about what you're leaving behind before walking away. It's all about mild, gentle cleaning when it comes to copper.