Using 3rd party popup instead of WordPress registration

I want to use a third party popup plugin to perform the initial registration of a user rather than them having to go to a further login box.

I asked the developer of the popup how to do this and they said;

“Unfortunately PopUp Domination is built for newsletter signups, not member registrations. If you are able to extract the form HTML that WP uses for registrations, feel free to try it.”

Their plugin has an option page that provides a place to enter code:
“Enter your html opt-in code below and we’ll hook up your form to the template:”

The guidelines they also quote are:
“You need to make sure the opt-in code that you have been provided contains the htmo <form> tag. Also make sure that it has both Name and Email address fields.”

Can anyone throw any light on how I achieve this please?

Many thanks, Graham.