…all you need to do is “map” your existing domain to your site. You will need an upgraded WordPress.com plan on your site in order to map a domain. Each paid plan comes with a free domain credit you can use to either register a new domain or map one you already own. You can map as many additional domains to the same site as you would like, but you have to pay for additional mapping upgrades separately.
Let me know if you have additional questions. Best Regards.