That depends... May need stitches if wound depth > 1/4”, wound edges are gaping or jagged or if fat / muscle is visibly extending from wound. If you can’t stop bleeding that requires medical intervention. See: http://www.mayoclinic.org/first-aid/first-aid-cuts/basics/art-20056711 When was your last tetanus shot?
Clean, then Vaseline. For small cuts, apply direct pressure for 10 minutes to stop bleeding. If this is successful, all you need to do is clean the area with soap and water and cover with plain vaseline and a band-aid. Repeat this once daily. There is no reason to use topical antibiotics like neosporin or bacitracin. Repeat daily until the skin heals over. If it becomes red, painful, or oozes pus, see your doctor.