Red Cross First Response medic here. This is what I'd do on finding someone lying unconscious, on their back, with a severed finger. Some of this doesn't apply to a fantasy setting, but I'll leave it in; it might be helpful to you or someone else reading this.
First up, DR ABC. Standard practice.
D: Danger. What caused this? Wild animal? Machinery? Sliding door? Is it something that might get me too? If so, sorry but I can't take the risk. If it's gone or been made safe, then I can help. If it's something I can mitigate or make safe without risking my own safety too much, then I do that, then start helping.
R: Response. See if she reacts to loud speech, then a shake, then sharper stimulus (squeezing the earlobe is a good one; hurts enough to wake up a groggy casualty, but no chance of actual injury). She's unconscious, so nothing here. Don't waste time; it's better they wake up while you're treating them than they die while you're yelling at them to wake up. If the pain stimulus doesn't do it, move on.
A: Airways. Nothing over the face, nothing in the mouth or nose, nothing blocking the throat. If appropriate, the recovery position will help keep the airways clear once checked, but before that, we have other things to deal with.
B: Breathing. Now we know there's nothing stopping the airflow, check for the rise and fall of the chest, see if you can hear or feel breath from the nose and mouth. To do all three at once: ear by their nose, cheek by the mouth, eyes looking down to watch the chest. You haven't mentioned that she's not breathing, so I'll assume she is.
C: Circulation. Not really much point checking thisonce we know they're breathing because if they're breathing they'll tend to have a pulse as well. At any rate, she's bleeding from a severed finger, so we can see that.
At this point, we're probably satisfied that she's not going to die in the next few moments, so we take a second to check for other injuries. We're looking particularly for head injuries here; anything that might have caused the unconsciousness that we need to worry about. Also worth checking for are signs of electric shock (burns, stiffness, nearby electrical equipment), poisoning (foam or residue in the mouth, odd-coloured skin, bleeding from mucous membranes like gums, signs of vomiting) and suffocation (strangulation marks, burst blood vessels in eyes). In the absence of all of those, I'd look at how much blood she's lost from the severed finger and decide whether it's enough to cause her to pass out. The volume of lost blood doesn't actually change what I'd do, but it's worth knowing, and the paramedics will need to know. If the blood loss is low, then I'd probably conclude that she fainted at the pain or shock of the injury.
Now we might want to put her in the recovery position. Things to consider here are whether there's any chance of spinal injury, and whether the position will interfere with access to things we need to treat. No problems with either, so recovery position it is. Wounded hand out, non-wounded hand to opposite cheek, wounded-hand-side knee up, and roll towards wounded hand. Non-wounded hand should now be between face and floor; wounded hand should be out in front of her.
Now we've dealt with the unconsciousness, we look to the wound. Severed finger. That's going to bleed and look scary, but it's not as bad as it looks. No massive arteries or anything, and on an easily-moved body part. So, as with anything that's bleeding more than we'd like, the first thing is to grab hold, find a comfortable way to grip that we can hold for a while without cramping, and clamp down. We're looking to squeeze the edges of the wound together if possible, and just press down hard over it if not. Next, we try to elevate it above the heart. It's on the end of her arm, so that's easy enough. Leaving her in the recovery position, we can pick the hand up so the forearm points straight up. It's not very far above the heart, but it's just a finger, so I'm not too worried. If it was the whole hand I'd probably lay her the other way over, wounded arm up, move the underside arm under her face (or use a handkerchief or folded jacket) and elevate the whole arm.
Now, if you have something cold and relatively clean, we might want to cool the wound - and, if we can find it, the finger. Ice works nicely, but wrap it first or you risk damaging it. Any fabric that won't shed bits will work for wrapping; I'm never without a cotton handkerchief, so I'd use that. Either I reach for the finger, or get someone else to do it - keep in mind we don't want to let go of the bleeding hand - and then we wrap it neatly and nestle it in an ice bucket or something. Likewise, ice wrapped in a clean cloth of some kind can be pressed to the wound, provided we can find a way of doing that without letting it bleed too much. Happily, a wound like this will clot before too long, so the bleeding should slow. The main aim here is to reduce swelling and tissue death to make for an easy reattachment, or at least to give them more viable tissue to work with when they close off the stump.
If she comes round at any point, my main worry would be shock - from pain, from surprise, and from blood loss. Keep her warm, don't let her get up or move around (not likely while I got my hand clamped over hers) and keep an eye on her for signs of her passing out again (not because there's much you can do about it, but because you'll want to know whether she's conscious at any given point). A warm and/or sugary drink can help too, although in this case I probably wouldn't do that because she'll need surgery for the finger and it's better if she goes nil by mouth before that.
