The only classes I know of (there must be others) are here:
http://www.wineschool.com/
He's been around a long time and is a well known figure on the scene. I can't speak from either first or even 2nd hand experience, nor can I comment on price.
My inclination would be to befriend a local merchant. Preferably the owner of a smaller boutique type store where they thrive on developing and cultivating personal relationships. By "befriend" of course I mean patronize. Be a good customer. They're not in it for the hugs or the conversation. Spend some money, hang out a bit on weekends when they're likely to be opening bottles. Taste. Ask. Almost all of them will have winery and distributor reps. in to talk about their portfolios. Sign-up for more formal special events which they all have. Keep a little notebook. Buy a good book or 2. Read. Taste.
Rinse. Repeat.
My first and current oeno-mentor was/is Howard Silverman at Howard's Wine Cellar on Belmont. Howard's father was one of the founders of Sam's but he struck out on his own after decades there. He's deeply opinionated, no one knows more.
My Italian wine mentor was Al Cirillo of Convito Italiano in Wilmette. He may well be retired by now. I used to work there, but no longer get up there at all. I'm a city boy.
People tell me that the folks at Wine Discount Center are very helpful and take care of customers very well. Somehow I've never been in.
Lots of people are close to individual staff members at Sam's. (You can't beat their prices, but I've got issues with Sam's. 'Nuff said for the present.)
There are many other little boutique stores including one on Clark in Andersonville, one on Lincoln in the Lincoln Sq. area, one on Halstead a bit south of Webster, I believe, and one on Southport near the Music Box as I recall.
Shaffer's in Skokie is very neophyte-friendly, and a friend of mine now works there part time.
Check out a few shops and see where the atmosphere feels congenial to you.
First thing I would do is pick up a Hugh Johnson Pocket Guide to Wine (about $15). He's a one-man industry of wine books (pocket guides, massive histories, glossy coffee table tomes and everything in-between). The Pocket Guide is about as easy-to-use, comprehensive and accurate as a small reference could possibly be. It lives in my shoulder bag.
Enjoy.
"Strange how potent cheap music is."