I wash and dry all the fabrics for quilts and iron before cutting pieces. They can be folded and hung on hangers to keep them ready.DON'T use dryer sheets in the dryer. These deposit a coating on the fabric which can prevent the iron-on to fuse to the fabric.
My younger daughter was making her first quilt, and after cutting out the pieces read the instructions telling her to wash the fabric. SOOO, she dumped them all in the washer with some sheets. Then they went into the dryer. We could hear thumping..and when removed all the pieces were in one lump, and directly into the trash basket. Very expensive lesson.
To wash small pieces, use a salad/lettuce washer with warm water, and if desired some mild soap...iron the pieces dry. This will work with precut pieces from a kit.