You don’t want to have users typing in your IP address to access your server, you want them to be able to access your server via the name you paid for. The exact steps to follow will depend on your registrar.
First though, a little background. When you register your domain, you only have the name reserved. When someone tries to access your website, they will still need to be told where to find it. That’s where a name server comes in, and the system that is used for this is called DNS — the Domain Name System.
Along with your name, the registration from your domain will say “if you want to know where this website is, you need to talk to this server”. You computer will then go to the domain name server and say “excuse me, I’m looking for your-domain-name, could you tell me where it is please?”. The domain name server will then say “of course, it’s over there”.
In general terms, most registrars also have domain name servers, but this may not be the case for you. If not, you will need to explore how to set up your domain with a different name server, but your registrar should have some information on how to do this. On the client page for most registrars though, you should be able find a page which allows you to add DNS entries.
Most often, this will be listed under the ‘Advanced’ section, and may say something about DNS zones. You need to add an A record (an authoritative record). Most providers will give you the option to add A records, MX entries, CNAMEs, and text. You may also be able to set NS entries. Your A record should be for your-domain-name, your-VPS’s-ip. You may also wish to add a CNAME for *.your-domain-name, your-domain-name.
This will allow you to configure subdomains on your server without having to keep fiddling with your DNS server. We’ll come back to your DNS server in a later tutorial on setting up email.