Brief procedure/overview, too tired to do details.
First, if your Plesk server is going to be the primary/secondary DNS server for that domain, then you will need to register your DNS server name(s) and IP address, again with a Registrar company.
Second, you register a domain name. The domain, of course, should be registered through a Registrar company (there are so many, but I use the more expensive Network Solutions, some use GoDaddy, Register.com, etc, etc, etc....) I do not endorse any of them, I leave it totally up to you to do your research on each and decide for yourself which one to use.
Third, you setup a Client in Plesk, then you add a domain to that client.
Fourth, build your web pages and upload them to the server.
Then once that is done, wait for the DNS for the nameserver(s) and domain to propagate around the world....
If you want to do something just as a strict limited demo, just for you and your 'client', then you could do the Third and Forth Steps, setup your workstation and client's workstation to use your Plesk server IP address as the Primary DNS server for Windows/Linux? and you should be able to 'browse' to the domain or IP address and see the web pages you created. Doing it this way, the domain will not be accessible by the rest of the world since the domain is not a registered domain on the internet.
Note: The third step also requires you to go through all the client and domain settings and make your appropriate selections.
If your internet connection does not have a static IP, then you will have to deal with that as a separate but related issue which involves dynamic DNS.
If you have your server behind a router/firewall, then you should search these forums for that topic and make sure you do your research (again) before beginning.
Buy/read a primer guidebook, read the Plesk documentation (all of it).
If all you have done is setup a client, that's fine. You should then proceed to the part about creating a domain above.
Additional note: if you are using the free download of Plesk, make sure you know what the limits of that version are.