Bandaging a pet's leg is a serious undertaking. It is very important how you do it. If you wrap it too loose your wrap will fall off easily, but if wrapped too tightly the animal won't only suffer discomfort, but if gone unnoticed they could loose the leg. That is why it is very important to know how to wrap an animal's wound correctly.
The first thing to do is to shave the wounded area. You want to shave far around it so that hair can't touch the wound even if laid flat. Usually shaving to three inches from the wound will be good enough, or for less risk of infection just shave entirely around the leg/stomach/chest.
Use a gauze square soaked in Betadine/iodine, and scrub the shaved area. You should scrub three or four times. Do not use betadine/iodine with alcohol, they will deactivate each other without killing any bacteria.
Now place one soaked gauze square on the wound, and wrap the vet-wrap around the leg or stomach. The wrap should fit closely to the skin, but you should be able to fit two fingers under the wrap with just a little stretch to it.
If this is a leg wrap, look at the pug at the top of the screen, click on the picture for a better view. The wrap goes fro around the leg and loops around the shoulders and to the other leg like a kind of sling. the way that this is set up will help to keep dirt from falling in from above, and it will ensure that the wrap won't fall off if it needs to be on for the whole day or more. The wrap should be changed every two or three days. Check it in 30 minutes, one hour, and three hours after wrapping and re-wrapping it to be sure it isn't too tight. The Veterinarians at my clinic were talking about how many pets they've had to amputate legs from just because the wrap was applied too tightly by the owner, which cut off circulation and killed the leg.
The first bandage should be replaced after the first day so that you can check for infection. Place a warm compress for ten minutes before re-wrapping. The gauze square soaked in Iodine should be replaced each re-wrap as well. If there are any signs of infection you should immediately take your pet to the vet.