Most individuals and smaller businesses host their web sites on computers owned and operated by companies specializing in web hosting. It is possible to host it yourself on your own computer, but unless you are really into doing all the technical set-up stuff and maintenance, it's probably more effective (and secure) to let the specialists do it. They have the equipment, the high-speed network, and the know-how and personnel to keep the system current, perform backups, etc. (Well, hopefully they do!) Most such hosting companies will provide the necessary service for you to purchase/register a domain name and have that domain point to your account on their host computer; and they typically have a suite of support utilities that you can use to manage your account and web site.
As to which service to use if you go that route, there are several threads already here you can search for, and of course thousands out there if you do a web search on something like "web hosting comparisons" or such.