As the school interviews New Media professors, this article might be worth reading. Be sure to read the comments as well. Keep in mind that what we've been learning in class would fit under the "right" way to learn the web.
If you're into gaming, you might find this web developer skill tree fun. While geared more towards "programmers", it can give you a good glimpse of the breadth of the web design/development field. For the record, I have only a few of the skills listed in the tree (and don't have a great desire to learn many of them).