Wordpress has two offerings: a self-hosted option available at wordpress.org, and a version that is hosted by Wordpress at wordpress.com.
If you'd like to use Wordpress for free, you'll want to choose the self-hosted option which is available from wordpress.org. You'll need to set up your site locally and host it yourself. A free hosting service may be found here.
If you'd prefer to have Wordpress host your site, you can choose the option available at wordpress.com. Using Disqus on a WordPress.com site requires a WordPress.com Business plan which supports third-party plugins like Disqus.
To install a plugin from the Plugin Directory, head to My Site → Plugins, and click the Add Plugin button. Search for "Disqus" and select the plugin authored by Disqus. Click "Install" and the plugin will be added to your site.
For more information on adding Disqus to your WordPress.com site, check out WordPress' documentation here.