To build a web site, you will first have to sign up with a web hosting service, which will allow you to upload your pages to your website.

There are two types of web hosting services. In one type, you will have to pay certain amount of money to sign up with that web hosting service and it will give you a domain name like www.yourname.com.

In second case, there is no need to pay the web hosting service. You will just have to sign up with that service and it will offer you free space for your website. In this case, your domain name will be something like “http://yourname.hostsite.com” or www.hostsite.com/yourname.

While selecting a web hosting site, check out whether the site supports FTP or not as it saves lot of time. (Click here to know about FTP.) 

I am giving a list of some of the web hosting services. You can select a service which is suitable for you.

http://www.crosswinds.net  
It offers from 1GB to 4GB space for storing your pages and files. It also supports FTP uploads, and upload of CGI scripts. But it is now a paid site.

http://www.oocities.org
The site provides 15MB free space. But you can get some more by paying a certain fee, which also includes FTP support and removal of advertisements from your site. This site is owned by "Yahoo!"
It offers domain name such as "www.oocities.org/yourname"

http://www.0catch.com (pronounced as zerocatch)
This site offers gigantic 100MB free web space for storage of your pages and files. It also supports FTP.
It offers a domain name such as "www.yourname.0catch.com"

http://www.tripod.com
The site gives 50MB web space for storage and allows FTP uploads with CGI support.
It offers domain name such as "www.tripod.com/yourname"

http://www.angelfire.com
This site offers up to 20MB web space. But it's site building tools are a bit difficult to use.
Both Tripod and Angelfire are owned by Lycos Network. But Angelfire fails to keep up with the latter.

http://www.freeservers.com
It offers 12MB of web space and an e-mail account. It's page building tool is quite useful.
This site offers domain name such as "www.yourname.freeservers.com"