Well... I'm 21; currently in college for a BS in CS, though I don't attribute any skills to this. I've spent perhaps the last five or six years learning Web development technologies, started with a little cryptography three or four years ago, been doing some low level data structures in C for the last year or two (little dabbles of software engineering in this time frame as well), and lately been learning the workings of enterprise resource planner software (the kind you get paid six figures to know).
If you want to build yourself to be very knowledgeable, simply enough, you have to read, use what you've read to build something, read some more, then do it all over again (parts of what you've already read will make more sense the second time around, once you already have an idea of how everything fits together).
Unfortunately, you can't read just anything you find. Any topic, especially one that is popular to the masses (like the Web), will have books, articles and tutorials that have been written by people who do not really know what they're talking about. Knowing how to find the best source of information is almost as important as deciding to learn, otherwise you will be spending considerably more time only to reach a lesser level of proficiency.
Technologies that have been carefully designed by a very specific group (e.g., languages such as HTML, CSS, PHP, Perl, C, C++, or protocols such as HTTP, FTP, SMTP, POP, etc.) will almost always have official documentation or a manual that is the best source of complete and accurate information. (Sometimes there are exceptions, such as SQL, because the actual implementations may be very different from each other and from the specification.)
Other examples where there is no straightforward manual is general fields of study in computer science such as data structures or software engineering. In these cases you have to find experienced people in these areas; a good place to start is the usenet newsgroups, but visit every reputable forum you can find. Ask these people "what is the definitive work for data structures", or "what is the data structures 'bible'" (or whatever topic you happen to be looking up). If you get a fairly consistent answer then you've most likely found a good choice. If you have indeed made the right choice then this should be the only book you’ll need. I find it interesting sometimes when people boast about having five or six books about Perl sitting on their shelf… (I have only one).