The *basic* process...
=> Get your WordPress managed hosting in place.
=> Install your theme and plugins.
=> Copy and paste the content from your HTML site into the new pages on WordPress.
=> Setup widgets, navigation, social media, etc.
Managed WordPress hosting provides a temporary URL for you to setup your site and work on it until you are ready to launch. All the while your old website with your domain is out there live until you are ready.
Once you have the site ready to go -- you change your domain's DNS to your Managed WordPress host and the new site will display.
Every site migration is different. I don't know the functionality of your HTML site or what you want on your new site, so your mileage may vary.