How?

Install a plugin for your site and configure it the way that best suits you.... That's it! Once your plugin is configured and running then new user registrations (and other events if supported) will be checked against the lists we have, lists details known hostile and abusive addresses. If a match is found then your new member won't get their foot in the door and won't be able to start posting on your site. If you would rather do checking offline then we provide all our data as downloadable files.

You can look at the ready to go plugins or the API documentation if you would like. There are a lot of downloadable files that provide a all the data we have in many different ways, and may well work with what you have in mind.