If it's a fairly even piece, maybe 1/4 yd, it's folded and put in a storage box. Pieces that are irregular go in a shopping bag, one for flannel, one for cotton.

If it is big enough to fold and still be able to see it in a stack, then I fold it. Fairly good size scraps are folded with the 'big' piece. I've started putting small scraps in zip bags of either similar size & shape, similar type of fabric (batik, oriental, corduroy), or by light, medium, dark.

#2, too!