I keep a basket on my sewing table, to collect scraps as I sew. I consider anything less than 1/4 yard to be a "scrap," and will save pieces as small as 2 inches square. When my basket is full, I organize the scraps by cutting the larger pieces into 12, 8, 6, and 4-inch long strips; I cut the longer strips first, and then finish up with the smaller strips. Width doesn't really matter to me, but it has to be at least one inch wide to be worth cutting. Depending on the size of the scrap, it may lend itself to being cut into squares rather than strips. Again, I cut the largest square I can, which is most often 6 inches, and work my way down to the smaller ones. I keep all the strips and squares sorted by size as I cut. This is the sort of task I do in the evening, as I'm watching TV or chatting with my husband, so it doesn't cut into my work time. (We quilters love to play with our fabric, so this is not considered "work!")
Once I cut all of the scraps in the basket, I have to decide what to do with them. Most often I put them in baggies, labeled by size, and keep them in the wire baskets in my quilt studio's closet. When I get a nice selection of strips and squares, they beg to be made into blocks. When I have enough blocks, Presto: I have a quilt! How painless is that?! Quilt teachers say that a "true" scrap quilt should be totally random --- just put your hand into the baggie and pull out the next scrap to sew to the previous scrap. As you may be able to tell, such total randomness is not in my nature. I have to arrange my strips and squares in a way that is pleasing to my eye. No clashing allowed!