It is a bit difficult to give an exact number of liberated prisoners (reasons for which I'll give below) but we can say that of the 714.000 recorded camp inmates in January 1945 at least a third died on "evacuation" death marches, i.e. on the marches the Nazis initiated to get these prisoners out of the camps before the arrival of the Allies. So about 475.000 prisoners were liberated in some form or other. Of these 238.000 victims of the death marches around 50% were Jewish.
In most camps the Soviets liberated, most of the prisoners had already been forced out of the camp on death marches by the Nazis, so only a couple of thousand prisoners were liberated alive in these camps, mostly those who were too sick to be evacuated or who had been able to hide. For example in Majdanek, the first camp liberated on July 22 1944, about 500-1.000 prisoners remained. In Auschwitz, which was a larger camp, by the time it was liberated on January 27, 1945 about 6.000 prisoners were found alive.
Quick side note: Apart from Auschwitz (and Majdanek depending on definition) the extermination camps were not active anymore by 1945. Aktion Reinhard (the largest murder action with 1.5 million killed in the three camps Sobibor, Treblinka, and Belzec) had been finished by the summer 1943 and all remaining extermination was done almost exclusively at Auschwitz.
With the Red Army nearing the Concentration Camps in the East, the Nazis forced the inmates to march westward into Concentration Camps in the Reich, which is why the majority of prisoners were liberated by the Western Allies either in the camps in the Reich or directly while they were on death marches. In the case of Auschwitz e.g. about 20.000 people were forced to march to the Bergen-Belsen camp in Germany where they part of the 60.000 strong group of prisoners liberated there by British forces.
One of the problems that arises with these numbers is that due to the conditions in the camps, the conditions of the death marches and the generally bad health of Concentration Camp prisoners, a considerable number of them didn't survive liberation for long. Having been starved and forced into overcrowded barracks, many were weak and sick. When liberation came, Allied troops often made an effort to help immediately but sometimes the help didn't help. If someone is starved it is not advisable - as many Allied soldiers did - to give them solid and plentiful food immediately because their stomachs can't handle it. Also, disease was a huge problem. In Buchenwald for example, British forces burned large parts of the camp because 10.000 former prisoners died in the aftermath of liberation from Typhus.
Also, a large number of prisoners were not liberated in the camps but rather on Death Marches. Such was the case in Bavaria where over 10.000 prisoners were forced from the camp on April 26, 1945 with over 7.000 of them later liberated near the German-Austrian border.
So the problem is that we need to assume the number of people who survived liberation for a considerable period of time is lower than the above cited 475.000 prisoners. Also, in regards to the accuracy of the numbers: They are largely accurate but provide always somewhat of an approximation since the liberating forces tended to count the liberated prisoners only approximately in order to be able to provide sufficient food and medical aid but they did not want to perform an accurate to the numbers head count right away since that would have distracted personnel from the aid effort and the remaining fight. We know these numbers to be largely accurate since they largely work with the later numbers of Displaced Persons who said to have survived the camps.
Sources:
Nicholaus Wachsmann: KL. A History of the Concentration Camps.
Dan Stone: The Liberation of the Camps.
Stefan Hördler: Ordnung und Inferno.