In both the respective parties rose to power through a combination of subversion of a democratic process and violence. In part, this occured during a period of both nation's history where the current government was severly weakened by war and economic collapse. The population was already inclined to want change due to these conditions.
In the Soviet Union the Communists subverted the Duma and the Social Democrats to gain power while simultaneously starting a civil war. The Nazis likewise got into power by a democratic process and then used violence (burning the Reichstag and threats that communists and other radicals were to blame) to usurp power and make Hitler a dictator. Both were also successful through their very orgainzed, para-military type, party orgainzation. Their opponets were less orgainzed using more open debate and democratic methods that led to disunity on many subjects. Democratic debate also greatly slowed responses to these autocratic political parties when the threat from them was realized. Thus, they could gain control before more democratic opponets could orgainze a successful counter to them.

Once in power both were minority parties that ruled through exclusion. Both used the cohersive power of government to control dissent (secret police, military intravention in civil unrest, control of the press etc) and prevent free speech. Obviously, they also quickly moved to restrict or outlaw political opposition to their rule.
Both also relied heavily on political indoctrination of the populace, particularly children. They did this through the school system and through government mandated participation in extra curricular activities like the Young Pioneers (Communist) and Hitler Youth (Nazis). This was done to help ensure new generations would be willing participants with the proper political views that supported the ruling party.

Oh, remember, plagerism is wrong.