Lets assume that you have a router hooked up to a static IP provided by your ISP and your server is hooked into the router. Your ISP will help you with the marrying the IP to your Registered Domain Name and you should be seen by all of the net within in 48 hours.
Normally its a package deal: domain name and fixed ip address sold by the ISP. They give you a sheet a paper with your ip settings for your router and your up and away.
If you don't have the luxury to afford a static IP you can go to NoIP.com or DYNU.com and fiddle around with that
Some of that probably has changed since I did a few some years back
I am confused by your statement "how to apply the domain name to the website I have made" Your domain name is linked to an IP address in whois, that IP address is linked to your router.
Hope this helps a little