Most Holocaust survivors were unable to return to their homes, or even their home countries. In Poland, many of those who tried to reclaim their homes were murdered or threatened with violence from their neighbors. In Kielce alone nearly all of the survivors who returned were murdered in 1946. Most had no families to return to, their homes and property had been stolen either by the Nazis or by their own neighbors. Most who tried to return home would leave soon because of threats to their lives or the pain of losing everyone they had ever known and loved. Some were hundreds of miles away from their homes. Antisemitism was still rampant. As they had before the war, the Allied countries barred Jewish survivors from emigrating, and the British Empire continued their policy of extreme restriction of Jewish emigration to the British Mandate in Palestine. Most Holocaust survivors remained behind barbed wire in displaced persons camps (DP camps, what we would now called detention or refugee camps). Many remained in DP camps set up on the sites of the concentration camps they were liberated from. These DP camps were run by various aid organizations and administrated by the Allies and the new UN under the United Nations Relief and Rehabilitation Agency (UNRRA) along with Jewish organizations like the Jewish Joint Distribution Committee. Some of these camps lasted until the 1950s. They only really began to empty out in 1948 when the state of Israel was established and immediately opened its borders to all Jewish refugees.
Most survivors liberated from camps, spent the initial weeks after liberation either hospitalized or still in concentration camps. As people's health improved, and people started to recreate social structures, they started to discuss with other survivors what their experiences had been. Most of the camps liberated in the British and American zones of occupation had populations of former prisoners made up of various groups who had been marched from concentration camps, forced labor camps, and the death camps of Auschwitz and Majdanek in the East, so they had experienced a wide variety of aspects of the Holocaust and were able to share those experiences with other prisoners. Although there were language barriers, the shared languages of Yiddish and Hebrew helped facilitate communication between survivors. Liberators heard these stories, aid workers gathered some information, and people among the survivors also gathered information. By 1946 some people were gathering survivor testimony. The Allies also gathered documentation from the Nazis which helped them make sense of some of what had happened. Organizations like the Jewish Joint also began to gather lists of survivors so that survivors might be able to reconnect with any potentially surviving relatives. Names were put up on lists in DP camps and reported on the radio in Europe, as well as in areas with large Jewish communities in the US and to the British Mandate in Palestine, and later the state of Israel. The Allied countries also showed newsreels of concentration camp footage for a few months in the summer of 1945, and many newspapers reported what information was known, as did radio news. A great deal of information was gathered for post-war trials. Survivors and Jewish communal organizations were absolutely central to gaining information of exactly what had happened in each different location, and who had been killed, and this work is still ongoing. Yad Vashem, Yachad in Unum and dozens of other organizations are still doing vital work of gathering testimony, interviewing witnesses, both perpetrators and bystanders, finding and honoring rescuers, finding artifacts, identifying grave sites, and identifying victims.

"Post-Holocaust Politics" by Dr. Arieh Kochavi
https://encyclopedia.ushmm.org/content/en/article/displaced-persons
https://encyclopedia.ushmm.org/content/en/article/about-life-after-the-holocaust
https://encyclopedia.ushmm.org/content/en/article/bergen-belsen-displaced-persons-camp
https://encyclopedia.ushmm.org/content/en/article/postwar-refugee-crisis-and-the-establishment-of-the-state-of-israel
https://encyclopedia.ushmm.org/content/en/article/aliyah-bet
https://www.jewishvirtuallibrary.org/aliyah-bet-1939-1948
"Commander of the Exodus" Yoram Kanluk
https://encyclopedia.ushmm.org/content/en/article/the-kielce-pogrom-a-blood-libel-massacre-of-holocaust-survivors