So the picture is helpful. It is a stage I recognize. First, you must cut many more feathers than look like have been cut in the picture. Basically, all around and down the back. The poo/pee oozes everywhere and it is much easier to clean and more sanitary for her healing. The routine that I carried out was done 3 times a day, if at all possible. To stop her from laying, first separate her if you can. I used a giant dog crate inside the coop so she could still see everyone, etc. I put only foods like corn, calcium chips....no layer pells or eggs...nothing with high protein. It came highly recommended from one of the "big wigs"
on this site to add a water antibiotic and so I did that as well. I covered with a darkening curtain, but anything to keep the general light out is good. I would face the kennel door away from the window and left it uncovered so she could still see everyone and outside and she could see them.
So, for the three times a day part; I brought out a large cup/small bucket of warm soapy water, preparation H (dollar store), triple antibiotic cream/ointment (dollar store!) rubber gloves, paper towels or rags, whichever you use. I used the rags or paper towels to soak and clean the area really really well. Gently. Then, I would apply antibiotic cream to the inner most parts and around and gently push them back in and hold it for awhile..she will relax even. If you are squeamish, you don't have to push in and hold, but, I found this most helpful. Also, you can keep track if you feel an egg or not by doing this. It may very well fall right back out, but, that is ok.
After that, and with your clean gloved hand, place preparation H all around the vent (the preparation H helps to shrink the swollen tissues...I tried the honey and I tried the sugar and never had any luck with them...the preparation H worked much better). The preparation H will sometimes get a bit on the prolapse and that is OK..I would kind of wipe it around the outside and if the prolapse was in, it would hit the top...don't worry.
Do not peel off the scab yet unless you suspect a big infection. I put the triple antibiotic ointment on it and it would keep it moist, which is good, but you actually want the scab to cover up the tissue underneath while it heals. I know that it is really really enticing to "speed up" the process, or that is how I initially felt, because by pulling off the scab, it appears that most of the prolapse will go back inside....it doesn't work. If you have a big infection or gangrene, that would be a different story, but this looks OK right now. You can smell the difference.
Anyway, this process went on three times a day for 2 weeks almost. When she started perking up and I could be around, I would let her out. you don't want them getting depressed...that doesn't help. The others would go over to her butt, but, out of 20 plus chickens, NO one wanted to go near the preparation H, but, one pull of that scab and her prolapse and you can be back at square one or worse, so be careful. Finally, the scab fell off for the most part with one of her soakings....at that time, or by the next day or two, the rest of the prolapse moved inside. I still continued the treatments until it was completely back inside (however, not pushing anything back in towards the end...you will almost kind of get a sense of when you should stop...your hens might not even be bad enough to push in...mine's ENTIRE sack was outside with an EGG IN IT...) The pushing is very gentle too, it is more like you are guiding it back in.
A bunch of the advice I got was actually from somene who PM'd me and so it is not in the actual thread and I can't find the email, but, you get the idea. I personally would not soak it too much as you are potentially inviting infection as well as softening the scab too much...plus if I got too much water on my hen she would shake as they aren't feeling that well. IF you can set up some sort of bucket that is just the size of around her but (like the top of the cup I would use) you could try sitting her on that. Just a thought. I just held her in a particular way so that her butt was hanging out in the back and I would poor the cup so it just washed around the vent area and then I would soak and gently cleanse with the clothes/towels. I wish you luck. Please feel free to write back as I know that I used a lot of support whe nI was doing it. I didn't regret it, even though she passed 3 months later because, it worked for the time being, she wasn't suffering and, she could have been that other 50/50 that don't re-prolapse after a good treatment. Now...she may not lay again for you, but, I didn't mind that. She was the kids girl and I just wanted her healthy. I hope this is helpful.