WordPress.ORG does not host any sites and you cannot connect a self-hosted site to a WordPress.COM site (except by a link but that's not really making them one site). It's one or the other.
If you want to use plugins, you have to install WordPress (from here) on a hosted server - they cost money. (There are a few free hosts, but they generally have many problems - so not a good way to go at all.) It's also possible to use WordPress on a local computer - but that won't be accessible on the internet.
Here's more info on how a self-hosted WP site works: