Step 1. Do not ignore it.
I'm a chronically ill bitch and a big proponent of "if you ignore it, it'll go away." However, I have found this doesn't work as well with wounds. So, here's what I use to keep myself as safe as I can. With the addition of my footer from my helth page.
I am not a doctor, nor am I your doctor. This is civillian-to-civillian communication.
Now, for all of these shoulders I'm standing on.
Here's some stuff I grabbed from the Merck Manual about lacerations, a.k.a cuts or tears. Stop bleeding by elevating the area if possible, then apply direct pressure with clean cloth, gauze, or fingers for "at least 5 minutes." I'm using a mix of the consumer and professional versions here. Consumer version says to apply pressure, professional says to wash the wound. I have no idea what to make of this, but I usually go with stopping the bleeding, as I'm not a professional and it's uncouth to bleed all over the carpet on the way to the bathroom.
Speaking of, wash with mild soap and water. Tap water is okay. Professionals would use saline, but obv most people don'thave access to that at hand. "There is no need to use hydrogen peroxide or alcohol for cleaning." The concern appears to be that strong agents would kill healthy cells.
For those that hit themselves or others--I find my kink and self-harm research tend to overlap--there's this chart intended to be used by police officers.
It goes without saying that this is intended for escalation. However, we can use it to point out the areas least likely to do serious harm when hitting ourselves with hands or tools.