Or go to Internet Marketing conventions :) Those are fun ... plus, it's a good overview of a little of everything, and a good place to meet contacts. If you're really serious, I strongly encourage going to at least one Internet Marketing convention.
You should start by subscribing to good newsletters and forums. There is a lot of great free content out there.
There are so many Internet marketing techniques to learn about. I would suggest identifying one technique (for example search engine marketing) and focus on learning everything you can about it for 2 weeks. Then choose another technique and learn about that for the next 2 weeks.
IMHO, do this before buying any books, etc. as there are just as many bad books as there are good, and learning for free online will provide you with the knowledge to tell the good from the bad.