Seconding Joann's or Hancock fabrics for classes. You might also see if your town has a community arts program. Our city's Center for the Arts has year-round programs for both children and adults that cover everything from photography to scrapbooking to dance. I've seen sewing and quilting classes listed a few times too.
Honestly, the only real training I ever had was middle-school Home Ec class, and everything else has been trial and error. Once you get the really basic stuff, there are plenty of YouTube tutorials and books to help with tricky things. I think sometimes, the best way to learn is just by doing something wrong a few times until you figure out the right way.
Also, your sewing machine might have a manual that came with it. If so, sometimes they have some basic sewing tips and instructions in there as well.