Once you've sent in a quote request and received your mailing instructions, you are ready to pack and send your disks to us! If you only have one or two disks, it's as easy as attaching your disks to a single piece of cardboard with a rubber band, placing them in a padded envelope or a plain manila envelope and dropping them in the mail.
If you've got "a lot" of disks (more than 5 or 6) you're better off shipping them in a cardboard box. To keep disks safe, it's best to keep them from moving around - bundling them inside a wrapper of some sort (a sheet of bubble wrap, Ziploc bag, paper, whatever is handy) will stop them from becoming damaged.
For really big batches of floppy disks, it's even more important to keep the disks from moving around freely inside their shipping container. Bundling the disks together inside a sturdy cardboard box is required. Ensure voids inside the box are filled with stiff padding material.
If you're shipping hard drives, it's important to bundle them in stiffer padding. Packing peanuts are terrible - they simply crush under the weight of hard drives and do little to protect your delicate electronics. Small-bubble bubble wrap, dense foam, and other squishy-yet-firm padding are best at protecting your drive.