This is outside the realm of WordPress. I’ll give you a basic answer that should help you figure out what you need to do.
The general idea is you will point your new domain names to point to your web server’s IP address. Then your web server will see which domain name is being called and then route it accordingly.
If you have a dedicated server, you’ll probably set A record which says send the domain name to this IP address. Most web-hosting companies have their own name server that you’ll point the domain names to and they’ll take care of the rest.
In Apache, you configure the Virtual Host (VHOST) file to route a domain name to a folder. Now many web-hosting companies provided an interface for doing this. In fact, many will not allow you to manually edit the VHOST because of their infrastructure.
The best thing to do is look at how to add multiple domains to your server from your web hosting company.