This can be done with a strip of gauze tied in a large loop, with knotted side under the jaw. The ends of the gauze are pulled to gently close the muzzle, then the ends are either secured at the back of the neck looped through the collar or if none is worn, behind the ears.
You can also do this by using a leash attached to the collar, brought forward and wrapped twice around the jaws, then held while grasping the dog by the back of the neck/scruff. Likewise, you would want to hold the end of the guaze muzzle to keep it from slipping off.
You then lift the dog by the nape, using your other hand to gently support the ribcage so that your hands are basically facing each other, leaving the rest of the dog to dangle. The reason for this life saving lift is that organs and spine often can be allowed to hang in a more natural alignment until the dog can be lain along a stretcher and secured flat, laterally (face forward, on the dog's side).
Any attempt at lifting the dog in the usual way--the Lamb Lift or the Belly Lift--can permanently injure the spine or internal organs.
As per article https://www.quora.com/How-do-you-safely-handle-an-injured-dog