Cave rescue if extremely difficult. It can take several days to get an injured person out of a cave. I am an active caver and have been through some formal cave rescue training. Oh, yeah, I was a member of the Niagara Frontier Grotto (Rochester, NY) of the National Speleological Society from 1998 through 2001. Before that I was a member of Sandia Grotto in Albuquerque, and since 2001 I have been caving around the world and in the Appalachain Mountains from West Virginia all the way down to Georgia.
Clearly, the first choice is self-rescue.
If a self-rescue is not possible, then cavers call out the rescue team. Many of these people have been through formal cave rescue courses. A rescue litter, thermal protection and medical equipment are carried into the cave, along with whatever technical equipment is needed.
Once the immediate medical needs are addressed, the patient is "packaged" in the litter. This "packaging" usually includes a very warm sleeping bag, helmet, goggles, and a waterproof outer barrier wrapper. Warm IV fluids can be administered if necessary. A urinary catheter may be needed as well.
Then begins the long and arduous task of removing the patient from the cave. Moving a litter through a cave is extremely difficult, and takes a team of 30 or more people. In open passageways, the litter is carried. In tighter passageways, the litter is dragged. Sometimes cavers lie down in holes in the floor so that the litter can be dragged over them so the litter doesn't get caught or doesn't fall into the hole.
When crossing canyons, sometime a Tyrolean traverse must be rigged. This can take many, many hours to rig, and many hours to transport the patient across.
Vertical sections require that the litter be hauled up or lowered down the pitches. You can imagine all of the ropes and hardware that would necessary to move a rescue litter and a team of 30 people over technical ground.
It should be obvious to you by now that a severely injured person will probably die unless he/she is close to the cave entrance and the terrain is not too technical. Evacuations can take several days. Most successful cave rescues involve simpled injuries like femur fractures or non-life threatening spinal fractures.
My caving first-aid kit is: (a) bivouac equipment and (b) duct tape. If you can't get out of the cave with a duct-tape fix, then you're gonna need to bivouac until help arrives. I always carry at least one carbide lamp for a heat source, a 24-hour supply of carbide, an insulated pad to sit on, and a space blanket to contain the heat from the carbide lamp.