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Wash your hands and stop the bleeding. Rinse the wound under running water. Look for anything in the wound. Put a bandage over the cut.
Wash up with soap and water to help prevent infections. Then hold a clean cloth or bandage over the wound until the bleeding stops. Don't pull off the cloth or gauze to check on the wound until the bleeding has definitely stopped. That can cause the bleeding to restart. If blood starts to seep through, and the cloth or gauze has gotten soaked, don't remove it from the cut. Simply add more on top, and keep up the pressure. A puncture wound is going to be deeper than a cut. You'll need to hold it under the water about 5 minutes to really rinse it out. Once you are finished, wash the area around the wound with soap. This could be dirt, splinters, the object that caused the wound, really anything that shouldn't be there. You don't want any foreign object in the wound, as it could lead to an infection, or prevent proper healing. However, if the puncture is deep and has the object that caused it still inside, leave that object in and go to the hospital. Removing it will cause more bleeding. If you do find something, don't use your fingers to remove it. Instead, a pair of tweezers cleaned in rubbing alcohol should be enough to get out bits that won't wash away. Be careful not to poke in the wound. Reaching your finger, or the tweezers, or anything else into the puncture wound will only make it worse. Put a thin layer of antibiotic cream over the cut before you put on the bandage. Make sure the bandage goes directly over the wound. If the cut continues to bleed, replace the bandage as needed to keep it fresh. You should also contact your doctor for additional treatment.