If you accidentally cut yourself and don't have access to band aids, gauze or even a butterfly kit, look for some super glue. You can use super glue for cuts in a pinch so that the wound heals and doesn't get infected. This is a permanent fix for cuts that are less than an inch deep and an inch wide. Using super glue on these kind of cuts will keep you out of the doctor's offices as well.
Stop the blood for the most part. Take a rag, paper towel, extra napkins, your shirt or whatever you have. Apply direct pressure to the area and if possible raise that part of your body above your chest. Apply the type of pressure you'd apply to a thumb tack when you're putting it into a wall.
Once the blood slows significantly, you're ready to close the wound. If you have the water, now would be a good time to use it. Pour the water over the open cut as this will clean it. If you don't have any, that's OK also. Squeeze the two sides of the cut together.
While holding both sides of the cut, add a small bead of super glue down the entire length of the cut. Hold cut closed for 3 minutes while the glue dries. If there was excess blood, repeat the process. The glue will stop most of the bleeding and it will close most cuts needing stitches.