Most of the things the hacker culture has built do their work out of sight, helping run factories and offices and universities without any obvious impact on how non-hackers live. The Web is the one big exception, the huge shiny hacker toy that even politicians admit has changed the world. For this reason alone (and a lot of other good ones as well) you need to learn how to work the Web.
This doesn't just mean learning how to drive a browser (anyone can do that), but learning how to write HTML, the Web's markup language. If you don't know how to program, writing HTML will teach you some mental habits that will help you learn. So build a home page. Try to stick to XHTML, which is a cleaner language than classic HTML. (There are good beginner tutorials on the Web; here's one.)
But just having a home page isn't anywhere near good enough to make you a hacker. The Web is full of home pages. Most of them are pointless, zero-content sludge — very snazzy-looking sludge, mind you, but sludge all the same (for more on this see The HTML Hell Page).
To be worthwhile, your page must have content — it must be interesting and/or useful to other hackers. And that brings us to the
