You need two things...
1) A host - a company that will physically host the site on their machines for which you will pay a monthly fee depending on how server space it takes up and much traffic the site generates.
2) A domain - this is just the unique name of the site which you will need to pay to get registered. This needs to be renewed periodically (every year?).
ISPs usually offer a small amout of web server space to their users so if you just want to set up a few pages that are unlikely to generate a lot of traffic you could use them and not have to pay for a host. And if you don't mind what the site's address looks like you wouldn't even need to pay for a domain. They might give you something like this for free...
www.yourisp.com/~yourusername
But if you wanted something unique like...
www.londonjets.com
You'd have to pay to get that registered.
Hosts often sell combine packages - web server space and domain name registration together. Otherwise when you register the name you'd need to get it redirected to your actual host.
Now when it comes to chosing a host - or a company to handle the domain registration - I'm afraid I don't have much experience on that front.