There are two basic ways to host a web site for free. I do not recommend it for anything except a personal page or two you are creating just for the fun of it. Even then, the hassles can be more than they are worth. You get what you pay for.
Option one: a few ISPs offer free web hosting for a few pages or a personal page with your dialup or broadband account. Log into your Internet Service Provider's site as you would to check your email via the web, and look around for "web space," "personal pages" or similar features. This sort of hosting will place your pages at a URL (address) like this:

http://www.ispsname.com/members/yourname/yourpage.html

Or perhaps:

http://yourname.ispsname.com/yourpage.html

Either way, it's doesn't look professional, and these packages always limit you to a small amount of disk space and a small amount of bandwidth.

Option two: there are many companies that offer "free" web hosting. I put "free" in quotation marks because, instead of charging you money directly, they profit from your pages. These providers place banner ads, popup ads, popunder ads and other frequently obnoxious moneymakers on your pages. If you don't keep an eye on your site, you might wake up to discover you are now selling things you don't want associated with your pages. In many cases, these companies also require that you sign up to receive advertisements from them by email in order to receive a free web hosting account.

If you are still interested, your least obnoxious and most reliable option is probably still geocities, a service of Yahoo that has been around for years. You'll need to read the page carefully to locate the free option, and your pages will have ads on them. If you want control over your pages, pay for real hosting. The web hosting market is extremely competitive; you can host your pages very well for very little money. See Web Hosting Ratings for reviews of the many different plans and companies available.

One more quick note: if neither of these options appeals to you and what you really want to do is post diary, journal or "blog" entries for the world to read, consider LiveJournal. As of this writing, they provide an excellent, ad-free place to post your journal entries, and they offer enhanced options at very low cost. LiveJournal is not appropriate for other types of pages.