If it is a basic quilting class on piecing: 3X18 ruler, rotary cutter and mat, sewing machine, thread, cords, extra bobbins(unless one is being supplied),pins, scissors,pen and paper for notes(or phone for pictures), money if you are ordering in lunch or need to buy something at the store. Most classes have a supply list for you when you sign up for a class.
If you are going to buy the little plastic iron at the LQS, I found that mine did not get hot enough for me. I wish I had saved my money towards the little diamond shaped metal one on a wand for appliqué instead. If irons are available I would use theirs. It gives you a break to get up and wait your turn and look at everyone else's progress.