So for the most part, directly after liberation, the prisoners were told to remain where they were and were supplied by the Allied forces with food and medical care.
For the most part, in the months after the liberation, the governments of the newly liberated European countries made an effort to basically transport their citizens who had been in the camps back to their home countries. In countries where this either was not possible or not desired by the people who had been in the camps (especially pertinent for Jews and Soviet Citizens), a system of camps was set up in Germany and Austria mainly (but also Italy) by the Allies where these so-called "Displaced Persons" (DP) could live and work until their repatriation or until they were allowed to emigrate to a new country (mostly Palestine/Israel and the US).
These DP camps as well as the care for Concentration Camp survivors after their liberation lay mostly in the hands of the United Nations Relief and Rehabilitation Administration (UNRRA), the predecessor of today's United Nations High Commissioner for Refugees (UNHCR). Founded in 1943, its mandate was to "plan, co-ordinate, administer or arrange for the administration of measures for the relief of victims of war in any area under the control of any of the United Nations through the provision of food, fuel, clothing, shelter and other basic necessities, medical and other essential services".
So basically, directly after liberation, the survivors were cared for by the arriving Allied troops. If one felt strong enough and wanted, they actually could leave and return to their homes but for many, they spent some time in the camp they were liberated in and then were either picked up by their government or transferred to one of these DP camps. These camps also held former forced laborers and POWs, making up the DP population in Germany, Austria, and Italy of about 7 million.
It wasn't so much a system to reintegrate the survivors mentally but more physically by providing them food and medicine as well as giving them the opportunity to await emigration or repatriation but if they wanted they were also free to go.
I hope this answers your question.
Sources:
Atina Grossmann: Jews, Germans, and Allies: Close Encounters in Occupied Germany. Princeton University Press, Princeton 2007.
Hitchcock, William I. The Bitter Road to Freedom: The Human Cost of Allied Victory in World War II Europe (2009).
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.
To add to the fine answers in this thread, Dan Stone has written a recent book ( The Liberation of the Camps ) on this very subject. Stone discussed this book on the New Books in Genocide Studies podcast where he explores this very depressing chapter in human history.
I hope this is in line with the subreddit rules:
In his book "The Nazis Next Door" Eric Lichtblau writes about treatment of camp survivors. Directly to the question - no, they were not just let go. Moreover, in some occasions they were put together with Nazi prisoners of war (meaning Nazi soldiers), and they were ruled by the same Nazi guards that did it before the end of the war.
http://www.npr.org/2014/11/05/361427276/how-thousands-of-nazis-were-rewarded-with-life-in-the-u-s