Remove any broken limbs attached to the loose bark. This will stop the nutrients in the live tree from being absorbed by dying bark and tree limbs. Do not try to fasten dying limbs back to the tree.
Tear off loose pieces of bark from the main injury on the tree. You do not want dead bark remaining on the tree. Using a sharp knife or gardening scissors, cut the bark down as close to the body of the tree as possible. Be careful not to gouge or cut into the tree.
Clean the area where the bark as been cut away. Soap and water is fine to use, but you can also ask your gardening store for tree salve. This salve contains nutrients to treat the open wound. Use your judgment on the amount of damage to the bark connecting to the tree to decide whether salve is necessary. If the bark has large or deep cuts, salve is a good choice. After cleaning, allow the tree to dry.
Sand the edges of the bark close to the tree body using fine sandpaper. The goal is to bring the bark smooth and flush with all remaining tree joints. You want to avoid having spaces between bark and the body of the tree that may allow rain in or attract pests while the bark is healing.
Wrap duct tape across the newly smooth bark and cover it. If possible based on where the injury is, try to wrap wrap the duct tape around the tree to hold the bark intact and protect it. Several wraps around will do the job, but be careful not to let the duct tape bind or pinch in on soft wood.
Survey the area around the tree. If the damage was done within a day or so, collect all the bark pieces you can find. Clean the wound as described in prior steps. Position the bark pieces back on the tree and duct-tape them back into position. Leave undisturbed to heal.