Ok, so it's not that easy pinning down the overarching main features here because Nazi rule in Europe was rather diverse with the main lines running along the West/East divide in Europe.

One of the main architects of Nazi rule in Europe was Werner Best. Best was an ardent Nazi, police chief and SS-Obergruppenführer. He is a crucial but often overlooked person within the Nazi system. Best was in essence the architect of the Security Police Model, i.e. he pioneered the approach of fusing the police with the SS. The Gestapo as we know it as well as the Reich Security Main Office combining SS, SD, Gestapo and regular police was his idea in how it was to be set up. The same goes for his approach on "preventive action" on the side of the police, i.e. arresting and interring people who were likely to become a problem before they became a problem. He is also the inventor of the concepts of the Einsatzgruppen as mobile police / killing forces made up of Gestapo and SS personnel forces in the occupied territories.

Within the scope of the question, Best is important because he devised a conceptualization of Nazi rule in Europe. These included territories under indirect control, territories under mixed control, and territories under direct control.

In the first category, the prime example is Denmark. Denmark had to cease control of its foreign and defense policy to the Nazis but was allowed to keep its own government, going so far as to have elections in 1943 from which the Social Democrats emerged victorious. Another example is Vichy France. Vichy France was nominally neutral and while under heavy German influence, it was in some ways allowed to make its own policy. The Ustasha's Independant State of Croatia or Slovakia also kinda falls into this category because despite being satellites of Nazi Germany, there was a government that in many of its decision was influenced by Germany but also didn't receive direct orders from Berlin.

In the second category falls most of Western Europe, in the sense that in countries like Belgium or the Netherlands, there were Nazi overseers and the Gestapo and other Nazi agencies operated freely within the borders of said countries but the native bureaucracy was allowed to remain in place and basically do its thing. So in Belgium for example we have Belgian officials continuing to operate the countries Bureaucracy from Social Insurance to rationing to policing it.

In the third category there are countries like the Reich Protectorate in Czechia, the General Government in Poland, the Reichscommissariats in the USSR and so on. There everything was taken over by the Germans and while some of the natives might have found themselves in subaltern positions, the running of everything was essentially taken over by the Germans. E.g. after the invasion of Poland in 1939, the Nazi administration sent several of the former district majors of the city of Vienna to act as majors of major Polish towns and ensure their administration.

Where what kind of administration was imposed was determined by a variety of factors, including the Nazis' racialist views of said countries, where they expected trouble, resources, and political circumstance of the invasion. In Poland, there was never any chance that some sort of indirect rule would be established since the Nazis viewed the Poles as subhuman. In Croatia on the other hand, the establishment of a satellite state was influenced by the Nazi leadership not wanting to commit any troops to an occupation when the invasion of the USSR was right around the corner.

Life for the non-Jewish, non-Roma inhabitant of these different territories of course differed in a variety of ways but there are some overarching things that can be observed:

The suppression of political opponents. With the exception of Denmark, where the Nazis took a very hands of approach, everywhere else, political opponents were in danger of being arrested, deported to a Concentration Camp, and murdered. Especially Communists and the Left but also supporters of a previous regime, Catholics, Monarchists, Democrats and certain brands of Nationalists were if they in any way acted against the Nazi occupation in danger of facing severe repercussions. In the case of Communists especially, it wasn't really necessary for them to act on their political opinion because they were generally singled out for persecution as the Nazis believed them to be an essential part of the "Jewish conspiracy" they set out to fight.

Another and probably even more intrusive feature of Nazi rule in Europe was forced labor. Nazi Germany experienced a massive shortage in labor starting in the 1936 and subsequent years. This was only compounded by the advent of the war and the many men who were drafted into the German Wehrmacht. Their solution for this problem was to recruit forced laborers in every territory they controlled or occupied to send them to work in Germany. It is estimated that in the years from 1939 to 1945 about 12 million people worked as forced laborers in Germany. At the height of the forced labor program, in August 1944, about 7 million foreign forced laborers worked in Nazi Germany, comprising about 25% of its total labor force.

The recruitment for forced laborers grew increasingly violent throughout the war and while in France, the Nazis might arrest the total of employees of a company to send them to Germany or exchange one POW for two forced laborers, in Eastern Europe, they basically raided whole towns or villages, often burning the village and then arresting everybody who was trying to flee to send them to Germany.

A third issue was, of course, food. Nazi Germany followed the policy of feeding the German populace at the expense of the people living in their occupied territories. In Greece, the Ukraine, and the Netherlands, this lead to famine and people starving to death, all so that Germany was able to provide its populace with the necessary amount of calories, making them the second best fed population during the war. The food shortage in liberated Germany in 1945 needs to be seen in that light. Cut off from its occupied territories, there just wasn't the labor force to feed the Germans.

This is not exhaustive but I hope it gives some insight in the nature of Nazi rule in Europe and I hope it answers your question. If you have any more, please don't hesitate to ask.

Sources:

• Hitler's Empire: Nazi Rule in Occupied Europe by Mark Mazower (2008).

• Ulrich Herbert: Best. Biographische Studien über Radikalismus, Weltanschauung und Vernunft 1903–1989. 1996.

• Richard Evans' Third Reich Triology.

• Martin Winstone: The Dark Heart of Hitler's Europe: Nazi Rule in Poland Under the General Government.