I'm assuming that the registrar with which you registered the domains is also providing you with name resolution (aka DNS server). So you should configure your new domain with the DNS servers provided by the company where you registered the domain.
You also need to tell the DNS server itself the IP address that it should point to. Now, if your web hosting provider gave you an IP address all of your own, you should point to that - or to put it another way tell the DNS server to point to the IP address of your first DNN portal.
Next you need to tell the web server of your web hoster to "accept" your new domain and "route" web requests to the directory where you have your DNN installation. Go to your web hosting provider's control panel and find your way to the "domains" section and add your new domain as an "alias" do your first one.
If you configure your DNN portals/alias stuff right all should work.