They did this by claiming that Christ was in fact not Jewish at all. He was instead Aryan, and the son of a Germanic legionary serving in Palestine at the time. William Shirer, in The Rise and Fall of the Third Reich, points to Houston Stewart Chamberlain as the source for this idea, which was adopted by the Nazis. Chamberlain's book, Foundations of the Nineteenth Century is paraphrased by Shirer thus:

His Galilean origins, his inability to utter correctly the Aramaic gutturals, are to Chamberlain “clear signs” that Jesus had “a large proportion of non-Semitic blood.” He then makes a typically flat statement: “Whoever claimed that Jesus was a Jew was either being stupid or telling a lie…. Jesus was not a Jew.”

Chamberlain's ideas were hugely popular and influential in Germany after his book was published in 1899. He corresponded extensively with Kaiser Wilhem II, became a naturalised German citizen in 1916, and was awarded the Iron Cross. By 1923 he had met Hitler and was an early member of the Nazi party, writing for their publications. When Chamberlain died in 1927, Hitler attended his funeral.

Of course, there were still considerable doctrinal problems with Christianity. Hitler is recorded (in Hugh Trevor-Roper's Hitler's Table Talk 1941–1944 as saying:

The decisive falsification of Jesus's doctrine was the work of St. Paul. He gave himself to this work with subtlety and for purposes of personal exploitation. For the Galilean's object was to liberate His country from Jewish oppression. He set Himself against Jewish capitalism, and that's why the Jews liquidated Him.

I don't know that everybody did it in exactly the same way, but one of the ways they did it was through a movement known as "Positive Christianity". This was kind of an interesting offshoot of the "Historical Jesus" movement that had been so influential in 19th century Germany. Positive Christianity was most forcefully espoused by the Nazi philosopher (yes, there were Nazi philosophers) Alfred Rosenberg. It sought to de-emphasize the supernatural elements of Christianity and to portray Jesus as a sort of neo-pagan heroic figure who strove to fight against the evils of... you see where this is going, right? Rosenberg was sentenced to death at Nuremberg and executed for crimes against humanity.

I'm not sure if I'm allowed to ask a question within a thread that may sidetrack the discussion but here goes:

How did the Christian values of the Nazis coexist with the more occult/heathen elements like the Wagnerian north-germanic folk lore tales and norse mythology?

If you read Hitlers table talk which is available free online Hitler specifically says that Christianity is a Jewish invention. The goal of which was too make men worship a Jew and that communism is just taking it to the second level swapping out the State for Jesus.