You can NOT use plugins with a wordpress.COM account. Wordpress.com offers a basic wordpress install with some extra additions, but you cannot customize it as much than if you install wordpress on your own server.
If you want to use plugins, you have to install the version from wordpress.ORG on either your own local machine or on your webhoster's server.
My tip: there are many webhosters that will give you a free hosting account that's more than enough to get started.
Just google for "free php hosting" and make sure the hoster you choose offers an autoinstaller for Wordpress. (I used freehostia.com in the past)
Note however that free hosters will often come with restrictions: they will either deactivate your account if you haven't logged in for a month or two, they won't allow Wordpress to send out emails etc. So if you really want to use a plugin, I suggest you buy a nice php package from a hoster close to you (so working in Wordpress is not slow because of long page loading times)