First objective should be to stop the bleeding. If you apply pressure to the wound, preferably by a clean cotton cloth, then the bleeding can get automatically stopped.
Once the bleeding has been stopped is when the wound or the cut should be cleaned. This is important as it helps reduce the chances of infection. You must wash the wound for at least 5 minutes with cool water and a mild soap.
Do not rub alcohol, hydrogen peroxide, iodine on the area because that will cause damage to the tissue and delay the process of healing. Use fresh cotton to dab the area with these items.
Most of the cuts heal by themselves after the initial treatment, as mentioned above is followed. The only thing that you will have to do is to prevent the cut from any infection caused due to exposure to dirt and heat.
However, if the cut is deep, then you must use bandage to cover it up in order to prevent any infection and also to help the skin heal up quickly. Depending on the kind of wound, apply the bandage.
You can use the moisture enhancing and the liquid skin bandages in case the cut is mild and these are readily available in any first aid box.
In case you are using cloth bandage, then ensure that the wound is cleaned every time a fresh bandage is applied. Once the wound is cleaned, make sure that the area around the cut is dried enough before you re-apply the bandage.
This will prevent any infection under the bandage due to heart and moisture. Further, you can also apply anti septic powder after cleaning and drying the wound thoroughly and apply the cloth bandage afterward. This is a good preventive measure against infections.
In case there are signs of infection already, then apply an antibiotic ointment on the wound and then apply the bandage. This will prevent the bandage from sticking to the wound and will also help in speedy healing.