Jamie, do you already have hosting for your WordPress site? And to be specific, is your WordPress site self-hosted, or are you using WordPress.com? If I understand your question correctly, you will need to point the domain name you purchased to your hosting/server.
Depending on where you are hosting your site, you may have access to cPanel, Plesk or some other dashboard which will allow you to change DNS settings. This is where you make the domain name point to the IP address of your server. Once this change has been made, it propagated or works its way through the internet, so that when you type the domain name it finds your website. The initial email you received when you signed up for hosting should tell you how to get to your dashboard.
If you site is hosted on WordPress.com, look for using Domain Mapping in the support area – https://en.support.wordpress.com/domains/