Well... If its not intentional... if it is I'm sure you already have everything planned out or should. But... If it is not...
1. DON'T Panic! The worst thing you could do is panic. Your sub is counting on you to be clam and manage the scene and whatever may happen.
2. First Aid. Remember that kit we just made. Go get it out of your toy bag. At this point some may say stop the scene all together. I say you need to assess the situation first. Obviously stop what ever it was that you were doing that caused the breaking of skin but it doesn't necessarily mean you have to stop and pull your sub out of head space if it is just a little nick. But that is just my opinion.
3. Might want to put on some gloves. I like to use the latex free ones. Its just easier to just buy those and not have to worry that I might be using the wrong ones on someone with an allergy.
4. Clean the cut with an alcohol swab and put a band-aid on it. You could also put a little ointment on it before the band-aid if you feel like it needs it to prevent infection.
So there it is... my four simple steps to cleaning up a minor accidental cut while playing.