Since the very beginning (1983) I have stored in folded stacks (approx. 12"x12") with folded edges to the front, by color, behind closed doors. Some of those stacks are too danged high by now, but most of this fabric is less than 2 yard lengths. I store flannels and obvious theme fabrics -- children's/holiday/patriotic/etc. -- separately. Backings, because of their yardage, are also stored separately.
I don't always have to pull out an entire stack to see if I have what I need since those folded edges face forward; that helps. As I really enjoy the 'auditioning' process, I also straighten up and restack whenever I have to pull out a piece or a stack.
A stash is a wonderful thing!! I have hundreds and hundreds of different fabrics even though many of them are only half a yard. Because of this I make quilt after quilt from just my stash and probably buy less than 6-7 yards of fabric a year now; a good thing as I couldn't afford it!!
Jan in VA