I know you use a curved needle, but not much else? My story takes place in the 'old days', before hospitals; my MC lives alone in the wilderness, so she would have the skills to take care of herself and her animals, which I'm taking to mean that she can take care of a pretty bad wound. The wound in question is a rip from being bitten by a werewolf. I'm just not sure of the logistics of stitching it shut?
In a rough environment like that, you're most likely going to just be doing a simple "whip stitch" (I imagine Youtube can provide an example) as carefully as you can without taking too very long. The wound will need to be carefully washed and if still not clean wiped out with a cloth of something, especially if it's an animal bite, and double especially if it's a magical animal bite.
If you have any alcohol or anything similar to peroxide or distilled water you're going to want to pour some of that over it to help with sterilization. The exception is that if it's bleeding too much you won't want to pour too much alcohol around it lest it get into the bloodstream.
It's important that the two sides of the wound lie flat against each other, so the stitches need to be small, close together, and tight. Any ragged bits of skin may need to be trimmed off first. The wound will need to be covered with some sort of pad to absorb moisture and pus, and likely squeezed or even lanced and drained a bit from time to time as it heals. Clean linen is of course the choice covering over the pad, but anything from tape to wrapped cord will do in a pinch. The wound should be mostly kept covered but allowed to 'air out' at least once every day or two.
If the muscle is damaged it may require some surgery, but in the wild you're probably going to have to just sew up the skin and let it heal underneath as well as it can.
The thread you'd want is dried and cleaned animal sinew, but if that's not available then a faster if usually inferior solution would be some sort of plant fibers; only specific plants are suited and it's generally more difficult to extract. Very strong cords are sometimes prepared from the intestinal linings of various animals, mostly felines (hence "catgut"), In believe catgut thread can also be manufactured but like animal sinew it takes prep time, cleaning time, drying time.
What sorts of materials would she reasonably have handy in the wilderness? What kinds of needles were in existence at the time in your world? Did curved needles even exist? It might be reasonable for her to know how to sew, as in many societies of old, it was expected that young females learn all sorts of handicrafts. Thus, she might have sewing supplies handy in order to make or mend her own clothing (assuming she wears clothing out in the wilderness).
Would she know about surgical and other medical procedures? Would she know about sterilizing a needle and what sorts of threads would be appropriate for stitching a wound? Or would she use a regular needle and thread to close her own wounds? Maybe she has seen something like this done in the past for reference, and saw that the doctor used some sort of alcohol to clean a wound or needle. Or it may just be instinct that drives her to sew the wound closed.
If I had no knowledge of medical procedures and was in the woods with a gaping wound, I'd likely pinch the skin closed and sew it up with whatever I had handy and hope for the best. (If the wound were bad enough, I'd hope I didn't bleed to death first, though.) Of course, that could lead to complications, which could further complicate your plot and add tension.
I think sewing wounds is one of those skills that was actually more well known in its way in the past. I'm not sure how far back the incidence of curved needles in surgery dates, but if it was a common practice in 'ye olden days', it wouldn't be unreasonable to assume that she would know about them.
Pretty much any sort of needle made in the wild is going to be carved or adapted from bone whether it's curved or straight, and bone works quite well so long as you're careful not to break it.
Before, I was speaking just to the process of sewing wounds, but it's worth noting that if the wound's bad enough, the internal bleeding needs to be stopped or at least slowed first with continued direct pressure. Depending on how deep and open the wound is, it may even be a painful but necessary step to stuff it temporarily with some substance like a non-absorbent woven material (otherwise it'll just bleed through) to stop blood from filling the area.
At some point though, the skin will need to be sewn shut evenly and well to prevent infection.
If no sterilization material whatsoever was available, the best method would probably be to wash the wound briefly in a stream you knew was clean*. Next step would be to boil some water, as much as possible but any amount will do, cover it somehow while it cools so nothing falls into it, and once cool wash the wound with it. If you can set it up correctly so none of the water will cross and mix, the water will cool much faster if the bottom of its container is placed in a moving stream.
*i.e. nothing dead upstream from it, slow to moderate current and decently deep, clear water with lots of plant life growing at the bottom. Quick and shallow streams may seem like they'd be really clean, but not without a lot of plants for filtration purposes. This water can also, in general, be consumed in small amounts without ill effects.