You won’t be able to install any plugins on WordPress.com. In order to do that you’ll need to move to the self-hosted version of WordPress that you can download for free at WordPress.org.
You will need to purchase hosting and domain. Some hosts can have WordPress setup for you as part of their hosting package.
I use SiteGround and quite like them. There are other equally as good options for hosting our there as well – my only recommendation is to go with one that specializes in WordPress.
Good luck!