First of all Hitler did not invent this theory.

Hitler participated in WW1 as a dispatch and would therefore spend a part of his time on the frontline. The guy absolutly loved it. Before the war he was a nobody, living in a homeless shelter and surviving selling paintings to the tourists in the streets.

Joining gave him a purpose, a real taste for war and love for his country. It is therefore obvious why the defeat of Germany would deeply shatter such a person.

What made it worse is the fact WW1 victory was more economic than strictly military (even though the allied would probably have won militarily with a bit more time), the peace was therefore not imposed by the winners to a defeated German army on the field but negociated by politicians while the German army was still more or less in fighting order. The troops learned about peace after everyone else and they just received the order to go home with all their equipment and weapons.

This did not go well with a lot of veterans who felt they had been cheated from a chance to turn the situation and beat the allies. They therefore searched for a scapegoat. They found one pretty fast in the person of Kurt Eisner (among others), an anti war politician who had spent the war criticizing the blood thirst of the high command and organizing strikes among the factory workers making ammunitions, Kurt Eisner was also Jewish. Seemingly unexplainable events + secret plot organized by a kabal of corrupted politicians + jews = perfect conspiracy theory.

This conspiracy became quite widespread because it was really convenient and sounded a whole lot better than "we lost".

As I said Hitler himself does not have much to do with it, he has been himself converted to it when tasked by his superiors to infiltrate the NSDAP and report on what they were up to to the military intelligence. There he met Dietrich Eckart who was a strong supporter of this theory. Hitler got totally convinced of it and his legendary oratory skills made the rest.

Source : Ian Kershaw : Hitler : A biography

What exactly did Hitler blame the Jews for?

Mostly the idea that Jewish bankers didn't fund the Kaiser well enough during WWI to make Germany win. But, as I'll talk about after this, that was just the latest in the "Let's hate us some Jews" train of thought in Germany.

What of their lifestyle/religion/other factors did he use to 'authenticate' this claim? I assume he must have said something more than a blanket statement that the Jews were at fault in order to convince so many people that this was the case.

Hitler didn't have to convince people of anything. German anti-Semitism is quite old, going back at least a 500 years. It's well-rooted, with prominent German historical figures like Martin Luther being quite avidly anti-Semetic. He wrote several screeds that were used as focal points during the Nazi rise to power.

Anti-Semitism was so ingrained in German culture that Friedrich Nietzsche saw it merging with Prussian nationalism into something horrible. It was the cause of his estrangement from his sister, who married a proto-Nazi, and eventually edited his works for Nazi propaganda.

Hating the Jews was really big in Europe, and the US as well, during that time frame. It was a very large attitude, and it took almost no real convincing to convince people of that. It's similar to the South and Jim Crow--it took no effort to convince the people there that keeping the black population suppressed was good, because they already believed it before that was even an issue.

Hitler just took the next step in a long history of anti-Semetic actions. Up until he sent Jews to the camps, Jews had been through absolutely everything that he did. Ghettos, wearing specific clothing, forced out of businesses, attacks on the street for being Jewish, etc, were all things that had happened in the past--for a number of them, some had actually lived through it before.

I believe it was Theodor Adorno who called the Jews "the middlemen of history." At any rate, the 'middleman minority' theory has been around for a few decades; it's an attempt to explain the Jewish economic role in Europe, the Chinese economic role in Indonesia, etc. Here is an overview, though it is dated (1973):

http://www.neiu.edu/~circill/benjamin/psci411b/theory.pdf

The 'middleman' is more visible than the elites at the very top, especially when an economy goes south. They make for excellent scapegoats. For example, if someone loses their house, or their farm or business goes under, because of abstract macro circumstances largely beyond their comprehension, the Jewish person to whom the loan was being paid off is more visible (and therefore more culpable) than the remote elites who run the political and financial institutions and who dropped the ball (for they were the ones holding the ball).

IIRC, there was some of this rhetoric circulating in the United States during the Great Depression. The likes of Father Coughlin (or was it Conklin?) would go on about "Jewish bankers in Chicago" being to blame for the plight of small Midwestern farmers.

In short – antisemitism is quite old, people in Germany were frustrated about the outcome of WW1 (look up "Dolchstoßlegende") which is why Hitler could've sold them anything and they would've believed him. Anything is of course a strong word, but it goes to show how much power/influence Hitler had in his early days even. Also, by building the Autobahn and providing people with jobs in the arms industry, he was very popular among the people.

In addition to the "ambient anti-antisemitism", I think it's worth remembering that Hitler didn't come to power over-night. There was over a decade of propaganda and indoctrination before the Holocaust.