A group called Genocide Watch (I attached the link below) has codified the eight steps of genocide, as you list them in your question. The list has recently been updated (also attached below) to include ten steps of genocide. The two additional steps are discrimination, which happens in step three, before dehumanization, and persecution is step eight, right before extermination. 

Discrimination occurs when a

dominant group uses law, custom, and political power to deny the rights of other groups.

The minority groups are powerless to fight back either legally or through other means. They have no recourse for this discrimination. 

Persecution happens when members of specific ethnic or religious groups are identified and separated specifically because of those identities. 

Their property is often expropriated. Sometimes they are even segregated into ghettoes, deported into concentration camps, or confined to a famine-struck region and starved. Genocidal massacres begin. They are acts of genocide because they intentionally destroy part of a group. At this stage, a Genocide Emergency must be declared.

You will have to do your own research to fully understand how the Holocaust fits the description of a genocide, but here are some thoughts to get you started using the eight steps you mention.

1. Classification: The Jews have always, it seems, been a people set apart and therefore open to significant persecution, In the case of the Holocaust, the classification of people was simply divided into two groups, the Aryans (Germans) and everyone else (the Jews, foreigners, gypsies and anyone else who did not conform to Hitler's definition of a Jew).
2. Symbolization: Germans wore the swastika as a symbol of their power and forced the Jews to wear the yellow Star of David as a symbol of their lesser social position. Homosexuals were forced to wear pink triangles, identifying them as another inferior group.
3. Dehumanization: The Nazi government decreed that Jews were an "inferior race," and that is how they were treated. Jewish businesses were boycotted, Christians were not allowed to marry Jews, Jews could not move freely throughout the country and strict curfews on the Jews were enforced.
4. Organization: The SS developed a plan to exterminate the Jews.
5. Polarization: The primary tool Hitler and his government used to accomplish this goal was propaganda, blaming the Jews for every conceivable woe in the country. [Take some time to research the propaganda techniques Hitler used; they were amazingly successful.] One other component which added to the polarization was the fact that any Germans who sympathized with the Jews were punished. These tactics worked.
6. Preparation: The primary way this step was accomplished was through separation. Jews and other identified minorities were sent first to ghettos and then of course to the concentration and work camps.
7. Extermination: Once the Jews and others were separated from the "true" Germans, the systematic killing began. These killings happened by work camps, gas chambers, firing squads, starvation, sickness, and more.
8. Denial: Bodies were burned (thus avoiding piles of corpses) or buried in mass graves (again to avoid showing any evidence of genocide). At the Nuremberg trials, German citizens denied knowing anything about the atrocities. [I've seen the camps, and people lived right next to many of them--they had to have known what was happening.] Even now, the German government claims only factions of the Nazi party were to blame.