Keep it clean and dry. I would keep it covered with the neosporin or just triple antibiotic ointment. Most wound clinic doctors order twice a day dressing changes (former wound care nurse!) I would keep the dressing on it until you see new skin covering the area. Beware that this skin is fragile so you might want to keep a dressing on it even after the skin forms. See a doctor if your finger becomes reddened, hot to the touch, or the pain increases. And definately if you have any drainage from the wound.