There are lots of articles on Now Smell This to help you get started, and I've also included some links to helpful information on other websites. Readers, please comment and add your best advice!
You're really brand new, and have no idea what anyone is talking about...
Start by reading the frequently asked questions. After that, you might take a peek at the glossary, then learn a bit about the basic building blocks of fragrance by reading on lists of fragrance notes, why they matter & why they don't and getting to know fragrance notes. If all of that starts to seem overwhelming, reading how much perfume knowledge is too much? might help you put things back into perspective.
Of course, you'll need to find some perfumes to smell, so take a look at our primer on how to get fragrance samples, free or otherwise. You might also want to learn more about how to apply perfume, and in case that new perfume isn't working for you, you'll need to know how to remove fragrance from skin.
You're learning more, but still worried your taste isn't up to snuff? Please read de gustibus non est disputandum ~ random thoughts on perfume snobbery.
If all of that wasn't enough, it's time for a trip to your local library or bookstore. Check out building a fragrance library: five "must-have" books for beginners.
You're a newbie, but can already feel the pull of addiction...
Congratulations, you're becoming a perfumista. You might find some helpful advice in things I wish I'd known as a newbie perfumista, part 1 and part 2. And if you've finished off those five "must-have" books for beginners, it's time for five suggestions for advanced readers.
Can you already see that your perfume collection is going to get out of control? We have lots of material on that subject; check out how much perfume is too much?, perfume for life: how long will your fragrance collection last? and curating a perfume collection. You can find helpful budgeting advice (especially in the comments) at perfume budgeting, part 1, part 2 and part 3.
More reading: Perfume 201 at Perfume Posse, the fragrance message boards at Basenotes, MakeupAlley, and Perfume Of Life, the bibliography at Scented Pages. And of course there are tons of wonderful fragrance blogs; check out the blogroll on the left right (it moved!) hand column as a starting point.
Update: a few more resources that you might find helpful ~
If you need help pronouncing names in French, check out the audio files at Bela's Fragrance Name of the Day.