My fat quarters and small (up to 1/2 yard) pieces are folded over a 3 inch ruler and put into boxes- I happen to have collected several boxes with attached lids that are the same size. They stack on top of a drawer unit in my closet. They're labeled "FQ" and I pull the boxes out onto the desk/floor when I want to find a fabric(s) that size.
Larger scraps that are odd sized or less than a yard, or really long (think trimmed from backing after long arm quilting) are stored in a drawer of the unit in my closet.
It's not a perfect system but it's the best I've worked out thus far.