Or, if you're super cheap/poor... buy some budget yarn (Cascade 220 is a great starter yarn) and some budget needles and teach yourself! There are tons of videos on youtube and ravelry.com is a great (free) resource, too.

If you want to go the class route... I highly highly recommend a sock class. I took one at another LYS when I was living in Philadelphia and it was great. Sock-knitting skills are really useful because they can be applied to a lot of different kinds of projects and even in a basic sock class you learn a LOT.

I agree with the youtube idea. I taught myself with a few books from the library and lots and lots of youtube videos. Really, though, it all depends on your learning style. Me, I prefer to experiment on my own whereas others need an actual teacher.

Oh, and this is a big one, LEARN CONTINENTAL NOT THROWING. Your hands will thank you later. And you can knit about three times faster. I had to teach myself continental a full two years after I learned throwing and I'm so glad I did.

There are so many excellent free patterns available online (Ravelry being a fantastic database of many of them) that knitting can be easily accessible for all. And I second DovieAnn's recommendation to learn continental style. But in the end, whatever works for you is worthwhile!

Once you learn how to knit, I recommend reading Knitting Without Tears by Elizabeth Zimmermann. She can help wean you away from patterns, and give you confidence to design your own projects.

I think I'll just second everything said in comments so far. A friend taught me the basics (knitting, purling, picking up dropped stitches) and much of the rest I've managed to pick up from YouTube, library books, and fearlessly blundering on and trying stuff. Unlike sewing, it's dead easy to undo mistakes, and it's way handy to have something to do whenever you're on the bus, waiting for a plane, or stuck in a dull meeting.

I love Alpaca Direct in Hayden Idaho! They have youtube videos too.
http://www.AlpacaDirect.com

I love these responses because I keep hoping to take a class but never get around to it (partly in fear of repeating my first traumatic knitting experience). Now I know it's possible to learn with the help of online videos, something I hadn't even considered previously, thanks everyone!

BTW, pie in the sky for a novice but something to aspire to, I'm really inspired by the designs done by the actress Karen Allen at:

http://www.karenallen-fiberarts.com/

Yes for teaching yourself, and also for having friends teach you. Basic learning is so easy- I learned from a friend after she came back from a year abroad. I am going to have another friend teach me Continental. The only classes I would take are those techniques that no one else is interested in, like I want to make a blanket in entrelac!

knittinghelp.com is a great resource for videos, and they also have an iphone/itouch app that is worth the money to download as it comes in handy when your knitting on the go.
A local yarn store is the best option to find quality yarns, but Michael's also has a few decent yarns for less money.
Ravelry.com is great for patterns, connecting with other knitters, and researching yarns.
Knitting is nothing to be scared of, once you learn the basics, it is very easy to learn new techniques, and it is great for gift giving. And yes "LEARN CONTINENTAL" ;)

Thx for mentioning continental, I had never heard of it. Getting off the computer and trying it out right now. :)

I learned how to knit at Artfibers in San Francisco years ago and very much enjoyed the class. Imagiknit is a lovely store with nice people and I've bought yarn there in the past!

While I never really advanced to anything beyond squares and rectangles, I do enjoy knitting so very much, and I'm content at my level, making scarves and blankets.

Personally, I'm the type of learner that learns a lot better in a class than learning through books or videos. I enjoyed having other people around me, learning from their questions, and having a teacher right there to correct me.

I only ever took the one class to get the basics down and since then have used books and the internet to learn a few new things or refresh my memory.