The Nazis used propaganda to spread their ideas about racial purity. They believed that Aryans (white people with blue eyes and blonde hair) were the Master Race as they were descended from the Ancient Greeks. Hitler thought that Germany had lost WWI because the race had become impure through inter-marriage. Racial policy became increasingly extreme from 1933-1945:

Discrimination: Jewish shops were boycotted from 1933.
Separation: The Nuremberg Laws of 1935 stripped citizenship from Jews and made it illegal for Aryans to marry or have sex with non-Aryans.
Persecution: Jews were attacked at Kristallnacht (Night of Broken Glass) in November 1938. Synagogues, homes and businesses were destroyed and hundreds were killed. 30 000 Jewish men were arrested and sent to concentration camps.
Extermination: During WWII, millions of Jews came under Nazi control. At first Jews were rounded up into ghettoes, most famously in Warsaw. Then SS Einsatzgruppen squads shot about 1 million Jews in the USSR. However this was felt too expensive and so the "Final Solution" was devised at the Wannsee Conference in January 1942. Extermination camps were then built which killed on an industrial scale. 6 million Jews and 2 million others (including Communists, gypsies and homosexuals) were killed.

The Nazis also developed the T4 "Euthanasia" Programme. This was an attempt to purify the German race. They forcibly sterilised 400 000 mentally and physically disabled people to prevent them having children. Then they began to murder them. Around 200 000 Germans were killed.

Why Racial Policy Became More Extreme

Pressure from below: the Nuremberg laws were the result of complaints from Nazi supporters that the government wasn't taking enough action against the Jews.
Working towards the Führer: senior Nazis tried to impress Hitler by devising more extreme policies.
World War II: this quickly put millions more Jews under the control of the Nazis. There were too many to cope with in the Ghettoes so the extermination policy was developed.

GCSE Germany 1890 - 1945 AQA

Racial Policy