Hi Federico, first of all Welcome to WebmasterWorld!
The first thing you have to do is to point the domain names to the server which should serve the pages of the sites. You an do that in to ways. The first way is to add for each domain an A record which contains the IP address of the server. In your case for both IP addresses the IP address you will use is the same. Sometimes a hosting company prefers that you don't use the IP address of the server, but a name they already have given to the server. In that case you add a CNAME record in the DNS settings of both domains which contains the name the hosting company has provided you.
You are now sure that all requests for both domains are directed to the webserver. How that server processes the website requests depends on the settings on the server. The server can run Apache webserver software, IIS software, or in some rare cases other server software. It depends on the type of server software and the type of account you have (shared or VPS) how the settings on the server should be. If you have more information about that, we can help you further in the right direction.