|developed by: Harold Goldstein -- -- http://goldray.com/
You can run a web server on your own computer but usually one finds a host with its own server; finding a webhost is comparable to finding an Internet Service Provider (ISP). In fact your ISP might very well become your website host so call them first! Many, like Starpower (was Erols), AOL, Verizon, offer a free site to its customers; that would be a good way to start. Also see PC Magazine's classified area, the Wash Post (or your local paper) Business section every Monday, the web (search for webhosts), in your Yellow Pages, etc. The book, Web Publishing with HTML 4, by Sams Publishing, also has hints (pg.764). Webmonkey has an article about hosting options under $10. I have used Fatcow successfully.
For sites with very basic needs, and willing to put up with some advertising, many hosts provide free space: try Freeservers (even w/your own domain), Geocities, Internet Trash. You can examine and compare from the lists maintained at Thefreesite and freewebspace.
The article and searching options at Webhosting Choice and the articles at WebHost Directory are valuable; or the webhosting talk forum; or search the huge indices at hostsearch, hostindex or tophosts.
You should have your host already lined up before registering your domain so you can indicate the IP# of your servers. Some hosts include registration with your new account so be sure to check. There are registrars that cost less; for example look at GoDaddy or check ICANN's list of accredited registrars.
Using an FTP program should be fairly intuitive and it will allow easy uploads and downloads. Here is a fine tutorial on FTP in general and WS-FTP in particular. And here are installation instructions for WS-FTP and while it assumes you are starting with a CD, it does explain the interface well. Ipswitch makes their userguides available online but it is for the pro version and is more than you need.
One thing to remember, while HTML files are text most other formats, such as gif, jpg and pdf are binary and the FTP mode must be appropriately set.
Alternatively, some html editing programs and tools, such as frontpage and dreamweaver, have built in file transfer tools. In some cases these tools require specific server capabilities (ie Frontpage requires FP server extensions). Consult the documentation that came with your software.