There are some important things that need to be done to heal a cut finger so that you minimize scarring and prevent infection. You want to make sure that you heal a cut finger in a certain amount of time too because the longer your cut is open the more chance you have for things to go wrong, and this means taking the right precautions and caring for your wound properly.
The first step to heal a cut finger is to clean and dry the wound and remove any type of debris or dirt that might be inside. If your cut is big enough to need stitches then you'd better let the doctor take care of that, but if it's a smaller cut you can do it yourself. Wash it with warm soap and water, and then dry it gently with a some sterile paper towel or cloth gauze and take care not to get fuzzy pieces inside the cut while making sure that all the dirt and any contaminates are removed.
At this point in order to heal a cut properly you need to put some hydrogen peroxide onto it so that any lingering bacteria inside is killed off which will help prevent any future problems with infection. To help with this even more you need to apply some Neosporin or the generic Bacitracin Zinc to the cut and spread it liberally around. This will prevent bacteria from growing at a later date and help to minimize scarring.
Next, you want to apply some type of bandage to help heal a cut finger which will keep it clean and keep dirt and any other contaminants out of it. Don't put the bandage on too tight and make sure that you use one that is large enough to cover the cut but not so big that it comes loose.
Change the bandage frequently and don't let it get soiled with dirt or anything else that could infect the cut or cause problems. Every day might seem like overkill for changing a bandage but you can never be too careful. Reapply the Neosporin or other antibacterial cream when you change the bandage and use Isopropyl alcohol or peroxide to clean the cut carefully.
Don't leave the bandage on for too long either. When you start to see that the cut is getting better it will most likely need to have some air getting to it in order to properly finish the healing process or the moisture trapped inside continually will keep the cut open and it wont heal like you want it to.