How did the Holocaust happen, from the beginning? A whole book would only scratch the surface. Basically, from 1933 (when Hitler was appointed Chancellor) to 1940, Jews were gradually alienated from society by a long series of incremental laws. First they could not hold certain jobs or marry non-Jews, then their citizenship was revoked, and finally they were stripped of possessions. In 1940, the first of several major ghettos were formed and Jews in cities were concentrated in them. By 1941, the Final Solution - plans to exterminate European Jews to the last - had been formulated. The Einsatzgruppen followed the Wehrmacht into Russia, and were tasked with the wholesale executions (by gunshot) of Jews, as well as Communists and other "undesirables." Gas chamber experiments began in 1941, and by 1942 several major death camps (including Belzec, Auschwitz, and Majdanek) were operating. The mass killings continued for several years, and by 1944 some camps were beginning to shut down for lack of victims. You can find a much more detailed chronology
here.
There is no exact record of the number of people murdered by the Nazi regime, as such records were not kept by the Germans. Furthermore, death was such a ubiquitous occurance throughout the Nazi system that even if they had attempted to record the number of deaths, it likely would have proved impossible.
The generally accepted estimate of Jewish deaths is between 5.5 and 6 million. The best and most detailed study of total deaths in the Holocaust that I know of is provided in
Death By Government, by R.J. Rummel. Total deaths were probably in excess of 21 million.
As for the links between the Holocaust and gun control and other contemporary issues? There are certainly some important ones.
There can be no doubt that Jews were prohibited from owning weapons. Gun control in Germany, IIRC was begun under the Weimar Republic in the late 20s in the form of a system of gun registration. Hitler took it and expanded it, though I do not know exactly how this was applied to the Jews. They were not a heavily armed group to begin with. By the time serious restrictions were bering enforced against them, exact gun laws were immaterial anyway, as the Gestapo was above the law. In an environment where you could be shot for looking cross-eyed at a Stormtrooper, being found with a weapon was a guaranteed bullet.
However, I am not convinced that mere possession of guns could have saved the Jews. It would have made them a more difficult target, certainly, but not an impossible one. The keystone of the Holocaust was the obediance of the Jews. As a general group, they were convinved that of they just bowed their heads and did what they were told, they would survive somehow. I'm afraid that even if some of them had been armed, the vast majority would have willingly turned in their weapons when requested to do so by the Nazis (I do not mean to imply that there was no resistance - there was more of it than many people think, and much of it was extraordinarily heroic - but only a miniscule fraction of the victims put up such resistance). They never imagined that the Hitler would really be willing to simply exterminate them. At the very least, they believed that they held some value to the Nazis as slave laborers. I did a bit of research on the subject of Jewish resistance, and Oleg was kind enough to
post it on his web site (thanks, Oleg!).
We have the advantage of knowing exactly what tyrants are capable of. I hope we can use that knowledge to make better decisions than the Jews (as a group) did.