Apply masking tape to your item if it is made of breakable material like glass such as a mirror or a picture frame. Masking tape is easy to remove without leaving residue on the glass and will help to prevent the glass from breaking by absorbing some of the vibrations. If the glass panel breaks in transit the masking tape will reduce the amount of shattering.
Wrap the glass in unprinted newspaper. You can usually get unprinted roll ends from any newspaper either free or very cheap. If you must use printed newspaper, put the item into a plastic bag first to prevent the newsprint from getting onto your item.
Cover your paper-wrapped item with a layer of bubble wrap. Tape the bubble wrap closed so it stays in place.
Choose a box that it large enough to give you an extra two inches on all sides of your item. Fill that two inches with crumpled newspaper. For extra protection mix some Styrofoam peanuts in with the crumpled newspaper.
Consider double-boxing the item if it is extremely fragile or extremely valuable. If you choose to double-box your outer box should be large enough to allow for another two-inch layer of crumpled paper between the two boxes.
Use good-quality packing tape to seal the package before shipping. You also might want to reinforce the corners of the box with the tape for extra protection from the box getting damaged in shipment which increases the chances of your glass breaking.