Disclaimer: I'm surrounded by doctors and medical books, but have no official schooling in the subject myself. The medical knowledge discussed below is the result of personal research with the attempt to improve fiction writing, not to cure and/or diagnosis people.
A really common injury, characters can get cuts from passing students in the hallway (no joke, I have a scar from the metal of a spiral notebook on my forearm) to fixing up a bike. That’s because cuts, and scrapes and punctures, are injuries to the skin. Which just happens to be the largest organ on the human body. But as it does rest outside of our body, it’s meant to take these injuries with no problem. After all, we don’t typically get serious injuries doing day to day things.
Types of skin injuries:
Scrapes – this is when only the top part of the skin is injured, and can hurt more than cuts simply to due to a wider surface area but they heal the quickest. Think skinned knees and rub burn.
Cuts – this is when the skin is actually opened, but that doesn’t mean blood wells up, simply that layer of skin are sliced. You can cut from practically anything, including plastic knives (don’t ask)
Punctures – this is when something stabs into the skin, traveling deeply into the body. Getting a shot leaves a puncture wound, though small, as does getting stabbed by a spear.
The help your character needs depends on how bad the wound is, which can be shown by the amount of bleeding. I think it’s a given that being shot is pretty major while the skin you leave behind on the court when sliding to hit the volleyball is minor, but if you have questions on specifics, you’re always welcome to ask.
As major bleeding can lead to shock, the character applying first aid should keep an eye out for that (if they know how, but even if they don’t, doesn’t mean you can’t have your bullet victim go into shock and scare his partner even further). Applying pressure to the wound is a must, and if the edges gap open try to keep them together. Pressure can be applied with hands (especially good if you want to write a graphic sentence about blood) or what ever is available cloth wise ( maybe a t-shirt to add some skin? Seeing abs can be a distraction from pain.).
Try to have the wound elevated above the heart to slow bleeding, and if there is something stuck in the wound DON’T TAKE IT OUT! It’s serving as a dam for the blood, items should only be removed by health workers. Granted, if the scene you’re writing is of a serial murderer’s kill, the killer might want to pull that knife out to witness the glorious spray of blood that would follow.
Most wounds will fall into this category, and I’m hoping your character knows the basics. Clean the would first, and apply pressure to stop the bleeding. Then wrap the cut, usually with gauze or in most cases a band aid. If the cut is long and you don’t have the gauze to wrap it, use a bunch of band aids moving across the cut so they can help hold the wound together.
Special note need to be taken of puncture wounds (like stepping on a nail). Allow the cut to bleed, it'll clean itself to avoid infection. Unlike cuts, which are caused by something slicing the skin and thus should be closed to prevent infections, puncture wounds are caused by something penetrating the body and thus there is already something in the wound – even if the nail you stepped on didn’t stay in your foot. And if the nail is still in your foot, take it out. Only if the bleeding is minor though, if it’s major, keep it in for the dam effect.
Granted, you’re character giving first aid could not know all then and then pull out the piece of glass sticking out from between a character’s ribs and cause his co-worker to bleed out. Talk about a traumatic, character defining moment.
Real life experience with cuts; tell us the most random thing you've been cut/stabbed with.