Plan ahead for weather during shipping too. Check local forecasts in your area and the destination area. If the temperature is going to be cold, tape a heat pack to the inside of the styrofoam container's lid. You can purchase these from camping supply stores or hardware stores, sold as hand or boot warmers. Be careful not to overdo it though, too much heat can destroy your coral frags before they ever leave your local shipping center.
Properly placing your frags in the bags is key. Placement depends on the type of frag also. For corals that are not attached to anything use a rubber band and attach them to a piece of styrofoam. It will float on the surface with the coral dangling upside-down, which will protect it from being smothered or crushed. If your frags are attached to a rock, rubber band the rock to a piece of styrofoam like before. If the rock is large, simply place it at the bottom of the bag. Mushrooms, unattached star polyps, and alike can be shipped loosely in the bag. Keep coral types isolated to their own bags so they do not sting each other. Make sure you give the coral 3-6" of water space too. When tying the bags, leave room for oxygen, or fill it directly with oxygen if it is available. Twist the bag closed, fold that part in half, and secure it with two rubber bands.
Always ship your corals overnight. Many people have been experimenting with different corals and their tolerances to shipping times, but do so at your own risk. Call your shipping provider and arrange a pick up time, or take the package to them. Always pack and drop off packages as close to the depot's closing time as possible, so the box sits for less time. Schedule A.M. delivery or pick up at the local depot for the receiver, so the corals don't spend all day in a truck. When the corals arrive just acclimate them like usual and monitor for signs of stress.
Pack well so the receiver can reuse the packaging that was sent to them to ship their coral frags to you.