Use a cardboard box, and cut holes in it for ventilation. Place something soft in the bottom, such as a towel. You can also use other types of pet carriers, such as cat carriers, if the bird is large. You should have something to cover the box or cage, such as a towel, as it is best to keep the animal in the dark and quiet. However, you shouldn't use a wire carrier, as that can cause harm to the bird. You can use either a heating pad (set on low) or hot water in a zip-top bag. If you use the heating pad, place it on the outside of the box at one end. If you use the zip-top bag, wrap it in cloth, and set it inside the box with the bird. Even small birds can cause damage to your hands. Put on a thick pair of gloves before attempting to help the bird. Before trying to move the bird, cover it with cloth to help calm it. Though the bird is injured, it can still cause you and itself harm if you startle it. It likely will fight back. Close the lid, and cover it with the towel. Keep the bird in a warm, quiet place while you work on your next steps. Make sure your pets do not have access to the area where you place the bird. Even with gloves on, it's important to wash your hands and arms after handling wildlife, as they can spread bacteria and disease. You will likely get the diet of the bird wrong. You can provide water so that the bird can drink on their own, but don't try to drip-feed the bird water. This way, the bird will be able to drink water even if it's dehydrated.
Have a box ready. Prepare a heating source. Put on gloves. Cover the bird with a towel or blanket. Pick the bird up gently. Put the bird in the box. Wash your hands. Avoid trying to feed the bird.