As /u/Evan_Th said, I have posted on the papacy during WWII before, focusing mainly on the allegations of silence made by Cornwell and others. That earlier post should cover most of the major details. As for the Vatican itself, there are two major approaches to evaluating its actions. The first is embodied by Zuccotti's Under His Very Windows, which acknowledges that many individual Catholics acted to help Jews but asserts that these acts were separate and discrete. The other perspective is elucidated by Thomas' The Pope's Jews which argues that the Catholics that took action were inspired (and sometimes funded) by the pope. Given the available evidence and testimony, I lean towards Thomas' conclusion. Many of the Catholics that acted specifically credit the pontiff for inspiring their actions, and I think that Zuccotti dismisses this evidence too quickly and completely. Both books are highly flawed--as are most of the books on Pius XII--by pursuing current political and theological agendas rather than focusing on the history.

For the papacy's stance on Nazism I would refer you to Mit Brennender Sorge, which was written by Pope Pius XII when he was still Cardinal Eugenio Pacelli under Pius XI. Many Catholics failed to listen, but some few courageous did heed the words of that encyclical:

Whoever exalts race, or the people, or the State, or a particular form of State, or the depositories of power, or any other fundamental value of the human community - however necessary and honorable be their function in worldly things - whoever raises these notions above their standard value and divinizes them to an idolatrous level, distorts and perverts an order of the world planned and created by God; he is far from the true faith in God and from the concept of life which that faith upholds. (8)

As far as calls for individual acts of conscience, we can look to paragraph 29 which says in part:

No coercive power of the State, no purely human ideal, however noble and lofty it be, will ever be able to make shift of the supreme and decisive impulses generated by faith in God and Christ. If the man, who is called to the hard sacrifice of his own ego to the common good, loses the support of the eternal and the divine, that comforting and consoling faith in a God who rewards all good and punishes all evil, then the result of the majority will be, not the acceptance, but the refusal of their duty.

It must be noted that the Catholic Church did play a part in contributing to antisemitism. David Kertzer's The Popes Against the Jews: The Vatican’s Role in the Rise of Modern Anti-Semitism does an excellent job of describing this phenomenon, but I think his bias affects his argument once we get to the 19th and 20th centuries. He ignores statements like the above, as well as Pius XI saying "Spiritually we are all Semites" and similar statements. Pius XII consistently called for an end to violence against noncombatants, and to assert that this did not apply to Jews is nonsensical in my opinion.

This topic is usually fractious, and few good books have been written on the topic. Most are assaults on the Church or defenses of it and came to their conclusions long before the evidence was considered. Ventresca's biography of Pius XII is one of a handful of works that are free of major issues. I would be happy to try to answer any followup questions, as this is a subject with a great deal of complexity.

There're several questions in the FAQ on this; I'd especially recommend these two by /u/Domini_Canes.

Wouldn't it be accurate to ask what their response was to Jewish persecution during the Holocaust? Since almost no one outside of occupied Europe knew that the Jewish people were being exterminated en masse.

Edit: I guess I may be wrong. I'll leave this up for posterity and for /u/JBWimo's comment.