The Danish word "skade" means injury or damage (like the English word "scathe") and "stue" is a room, so "skadestuen" is literally the injury room ("-en" or "-et" at the end of a noun means the definite article "the"). A less literal translation is "the emergency room" (the TV show "ER" is "Skadestuen" in Denmark).
We had our first trip to the emergency room with Sean.
On Wednesday night, he was walking back from the grocery store with us. He was doing a great job walking and holding his parents' hands. Holding hands is something very new for him---previously he wanted to be so independent that he would melt down if we took his hand. Without holding our hand, though, the city doesn't offer him many chances to walk, so he spent a lot of time in his stroller or being carried. However, on Wednesday he finally seemed to realize that as long as he held a hand he could walk forever. (I also think he was able to imagine that he was leading us.)
It was too bad that he got scathed right when he was learning to take our hand. He was walking near our house when he stumbled and fell, all the while still holding onto his mother's hand. He immediately started crying. He knows enough words now that he could tell us what was wrong ("elbow", though he uses that word in general for the whole arm), and he says "ow" when he's hurt. There was obviously something wrong with his elbow---he cried about it and would not move his left arm at all. So this was our second major opportunity to deal with the Danish health care system.
In Denmark, for everything except emergency room cases, one normally contacts their family doctor first (for emergencies, you just go to skadestuen, though you should call ahead of time or on your way there and put yourself into the queue to be seen.) In the evening or at night, when the family doctor is closed, there is the "vagtlæge". Literally, this is the "guard doctor"---it's the night doctor who handles cases that don't exactly warrant skadestuen but won't wait for the family doctor in the morning. You also call vagtlægen before going---I don't think they will see you if you haven't called. Presumably this is so they can tell you to wait until the morning if it's not really serious. When we called and described the situation, they told us to come in and have it looked at.
After a quick bus ride and a short wait, we were seen by the night doctor. Sean probably had a subluxation of the elbow. That is, the elbow joint was partly dislocated. The doctor explained what happened, gently stretched the arm, and Sean seemed more comfortable (though still in pain) and even started bending it. We took him home, gave him Panodil (think Tylenol) and put him to bed.
Thursday morning, it still seemed very sore and he was now not using that arm at all. We called our family doctor, and after hearing the problem she told us to call the emergency room and try to go there. The emergency room told us to come in.
At the emergency room, we waited to be seen. Sean was in a good mood, laughing and playing (though with his left arm hanging dead at his side). He was examined by the doctor who thought it would be all right and confirmed that it was probably an elbow subluxation (see here or here). They did take X-rays of the arm to be sure about it, though, and everything looked fine on the X-rays.
All in all, it was an OK experience. All we needed was Sean's CPR number. There was no paperwork, and there will be no bills (or rather, it's all rolled into the tax bill). In retrospect, it was good to learn how to call vagtlægen and skadestuen, and how to get there, without having a really serious emergency. The system seemed to work fine for us, and it is really pretty easy but it does take some experience to understand how things are "normally" done.
Sean is doing OK now. His arm still hurts and he will need a week or so to get back to normal. He needs more help to play now (he can't do anything except run and swing at the park and he needs help swinging; he's not able to do much with his Duplos one-handed).