It sounds like your hen has a prolapsed vent/oviduct. That problem can be hard to treat, but don't give up hope yet.
The first thing you need to do is isolate her from other birds. Chickens really enjoy picking at red, fleshy material, and if she is left with other birds, they could kill her. Put her in a darkened area--the idea is to discourage egg laying, which will aggravate the problem. If the protrusion is dirty, soak her lower half in warm (90-95 degree F) water and try to clean it off as well as you can.
It is possible that just a warm water soak will relax her muscles and allow the tissue to recede. If not, though, remove her from the water, pat dry with a towel, and examine her further. As long as the protrusion doesn't seem to have been damaged too much, there is a pretty good chance that she'll live.
What you need to do next is apply something to the protrusion to reduce swelling. Some natural remedies include honey and Witch hazel, or you can use Preparation H. Apply whatever you choose to use to the area, try to push the protrusion into the body once, and then leave her alone. More handling/pushing will only lead to irritation.
Once you have finished applying and pushing, put your hen back in the darkened area. Give her some water and layer feed. It is also a good idea to offer some form of a calcium supplement, such as a Tums, oystershell, crushed egg shell, or a water soluble powder. Calcium strengthens the muscles of the oviduct, which strengthens the area and helps pull tissue back inside the body.
Check back on your hen every few hours. If the protrusion hasn't receded each time you check her, apply more Preparation H, Witch Hazel, Honey, etc. and try to push the protrusion back in. It may seem like nothing is happening, but prolapses due usually eventually recede with few problems. In my experience with one prolapsed hen, it took three days of soaking, pushing, and applications to get the prolapse back inside. Ever since, though, that hen of mine has been healthy, productive, and otherwise normal.