So, when the allies -- Western Allies as well as the Soviet troops -- first liberated the camps, most of them were completely shocked. The Soviets had liberated camps well before the Western Allies starting in July 1944 with Majdanek and moving on in January 1945 to Auschwitz. The first camps liberated by the Western Allies were Natzweiler in Alsace, liberated by French troops in November 1944 and the Ohrdruf sub camp of Buchenwald, liberated by US troops on April 4, 1945.
As I said, the first reaction to liberation was shock. In the Soviet case, the camps they came across were mostly empty by the camps standard because the Nazis had moved the prisoners west before the Soviet troops arrived. In Majdanek about 2.000 and in Auschwitz about 6.000 people were liberated, most of them too sick to be moved by the Nazis or having hidden themselves in the camps. The shock and horror they encountered is apparent in an essay by Vasily Grossman, a Soviet writer who witnessed the liberation of Majdanek and then went on to describe the extermination camp of Treblinka, whose remains Soviet troops encountered at the same time as they liberated Majdanek.
Grossman - under the impression of what he has seen at Majdanek - writes "Stories of the living dead of Treblinka, who had until the last minute kept not just the image of humans but the human soul as well, shake one to the bottom of one'sheart and make it impossible to sleep. The stories of women trying to save their sons and committing magnificent doomed feats, of young mothers who hid their babies in heaps of blankets. (...) Inhabitants of the village of Wulka, the one closest to Treblinka, tell that sometimes the screams of women who were being killed were so terrible that the whole village would lose their heads and rush to the forest, in order to escape from these shrill screams that carried through tree trunks, the sky and the earth." Grossman also suffered a nervous break down after writing this piece and took several weeks to recover.
Western Allied troops had a similar experience. Seeing the emanicpated bodies of Concentration Camp prisoners who had been starved by the Nazis for weeks, witnessing their exhausted and tortured state, and hearing them recall the horrors of the camps left a very deep impression with liberating troops. In this letter, Aaron A. Eiferman, soldier of the 12th Armored Division, describes the liberation of the Dachau sub-camp in Landsberg. Writing among other things that ""We have seen what can be called the living dead (...) the sight that hit me was more than a person could express (...) It was to much for me, for I had tears in my eyes."
In the last camp liberated, the Ebensee camp, US soldiers came to face inmates who had been forced to use their frozen comrades bodies' as mattresses and were there also had been cases of cannibalism in the last weeks of the war. The shock was profound. So was the logistical challenge of providing thousands of people with help.
Under this impression, the first aid given was often food and very basic medical care in order to ensure the survival of as many prisoners as possible. Especially the troops that liberated camps often made it their first priority to give food to the liberated prisoners, sometimes with dire consequences. The body of a person who has been on a starvation diet for a long time is not able to immediately process solid food for some time. A considerable number of people died right after liberation after they had been given army rations by the liberating troops simply because their bodies went into shock from the sugar, fat etc. Only with the arrival of medical personnel shortly after liberation, did this practice cease in many camps and a proper diet to nurse prisoners back to health could be instituted.
Another problem was disease and housing. In many camps, but especially Bergen-Belsen, which had been used as a camp to collect prisoners from death marches in the last weeks of Nazi rule, typhus broke out. The typhus epidemic was so severe in fact that British burnt down virtually all of Bergen-Belsen after the prisoners had been evacuated. /u/TheTeamCubed talks more about it here. They also discuss the idea of providing psychiatric care, little of which was implemented.
In the first weeks after liberation about 10.000 people died in Belsen alone from various causes without the Allies being able to help.
Aside food and immediate medical care, an important part of what some termed "medical liberation" was hygiene. When at the end of April a twelve-strong Relief team of UNRRA personnel and Quakers arrived in Belsen they wrote that "little nursing is done at all since it was necessary to concentrate on trying to keep the patients clean, warm and fed, no easy matter when diarrhea is prevalent and hot water almost unobtainable." They set up a system of delousing the prisoners with DDT in order to prevent even more people becoming sick with typhus - something which terrified the prisoners because so many were traumatized about coming in contact with medical personnel with chemicals.
The same team also re-estbalished a water supply and provided small quantities of solid food together with a high claorie mixture designed to enter straight into the blood stream of prisoners unable to eat solid food and also designed to prevent diarrhea. Another issue was clothing, which the Allies had to supply in great quantities since as one of the British officers in Belsen described: "They (the liberated prisoners) were clad in filthy rags and were crawling and grovelling in the earth for bits of food.
Despite all the problems and criticism of the early effort, Dan Stone summarizes: "In fact, the medical relief operations at the camps liberated by the Western Allies accomplished a great deal, when one bears in mind the logistical difficulties of providing food, medicine, and clothing while the was still on." He goes on to cite Paul A. Roy who, briefly in charge of Dachau after its liberation, set out the scale of the challenge:
We had more than 32.000 human beings on our hands who, for years, had been treated worse than animals. Our first job was their welfare. We had to nurse them back to health, and to rehabilitate them mentally. Many of them had been so completely starved that the fatty tissue surrounding their nerves had been used up, producing a kind of nervous short-circuit. They could not think consecutively. Some of them had lost their memories, and their mental reactions were very slow and childish. They were human wrecks who had to be salvaged
Questionable language aside, Roy's words describe that here an institution designed to fight a war against Germany suddenly found themselves caring for thousands of liberated former prisoners who for all intents and purposes were in the most terrible state a living human being can be in. After an initial period of problems, the Allies managed to built an infrastructure of care and help for these prisoners and despite the great strain of doing so while the war was still on, managed to do so in a rather amazing way.
Another goal -- initially not as important as the medical care focused on survival of the former prisoners -- was housing. At first many liberated inmates had to remain at the former camps until they could be moved to new accommodation. For the purpose of housing and also repatriation to their former countries of origin (that was the original plan but many refused to go back, especially if their former home was in the Eastern bloc), camps for the so-called Displaced Persons were set up. These camps established at various sites all over Germany were intended to house the former prisoners as well as others such as former forced laborers. Being fed with 1500 calories a day and being given the opportunity to work for the Allies or in the local economy, there were thousands of these camps where people awaited repatriation or emigration to the US or Palestine. Run from October 1945 on by the United Nations Refugee Agency, UNRRA, these camps provided housing, foo, and medical care for about 850.000 Displaced Persons. Many liberated Jews waited there for a long time to emigrate to Palestine and from 1948 to Israel or the United States. The last of these camps were closed in the late 1950s.
Sources:
Dan Stone: The Liberation of the Camps.
Shephard, Ben. 'The Long Road Home: The Aftermath of the Second World War.' (Bodley Head, 2010).
Stefan Hördler: Ordnung und Inferno. Das KZ-System im letzten Kriegsjahr. Göttingen: Wallstein, 2015.
Nichaolas Wachsmann: KL. A History of the Concentration Camps.