The Nazis were (and still are) almost universally considered "far right". Nazis doctrine focused strongly on the following tenets, all of which are considered hallmarks of far-right ideologies:

extreme nationalism/patriotism
desire for a return to a previous glorious era (eg "make our country great again"), and linking themselves to that era
hatred of "foreigners", ie, racism - in this case, Jews and Slavs (Russians, Polish, Serbs, etc).
anti-communism, anti-socialism
anti-liberalism, and a general disdain for democracy
militarism, and glorification of the military, its lifestyle, and its victories.
"traditional values" (eg, dad works, mom stays home to raise the family, homosexuals are deviants who should be eliminated, opposition to miscegenation, and so on)
"Might makes right" and "if you aren't successful, it's your fault because you aren't trying hard enough" mentalities.

However, it's noteworthy that they also distrusted traditional conservative movements. They felt that the conservative parties in Germany in the 1920s had catered too much to Jews and leftists, and allowed Germany to be weakened. So while the Nazis were decidedly right-wing in outlook, especially once in power, early on they tended to claim they were actually "third way" (not left or right), or "syncretic" (borrowing ideas from both sides). However, Nazis were fairly pragmatic, so their distaste for conservatism did not prevent them from cutting deals with those parties. In 1933, conservative political parties were key allies that helped complete the Nazi Party's Machtergreifung ("seizure of power").

When it comes to economics, the Nazis, and their leader Adolf Hitler in particular, didn't really concern themselves too much with them (Hitler once basically said that economics were boring and a waste of time). They largely kept in place the old capitalist system of the previous regime, although they did pass some pro-corporate legislation (such as eliminating unions, lowering minimum wages, and forbidding workers from quitting their job without their boss's approval), and especially tended to favor the corporations that supported their regime. Those that didn't support the regime sufficiently or, worse, were owned by "foreigners", were occasionally liquidated- but it was for purely political reasons, not due to socialism/communism. On more than one occasion, Hitler did give speeches decrying Western capitalism- but this was more due to racism than any sort of Socialist notions. He believed that Western capitalism was being corrupted by Jews, and wanted to purge them from it.

What makes it tricky with the Nazis is that:

Before they came to power, they did occasionally say things that made them sound pretty left-leaning. In particular, the "National Socialist Program", passed before Hitler took full control of the party in the early 1920s, does have some very leftist sounding stuff in it. However, once in power, they conveniently "forgot" all the leftist stuff they had said, to focus on the list I provided above. Hitler was also quietly cutting deals with powerful businessmen throughout the 1920s, procuring funding and support for his rise to power. These businessmen were fearful of Communism and Socialism and Hitler's opposition to those- and his willingness to use his Nazi stooges to fight them- appealed to them.
People tend to focus a little too much on the name. The full name of the Nazi Party is the "National Socialist German Workers Party". Sounds pretty leftist, right? Especially since "Socialist" is right there in the name! Well, that doesn't really matter. Is the "Democratic Peoples Republic of Korea" a democracy? Anyway... there were a lot of parties in Germany in the 1920s that had leftist sounding names but weren't leftist at all. Hitler added "Socialist" to the name purely for advertising purposes- he wanted to make his party more popular.
Before 1934, there actually was a leftist wing of the Nazi Party that believed in some socialist ideas. Most of the time when you see a quote on the internet from the Nazis or Hitler and it sounds super leftist, it's because it's actually from someone from that wing of the party. Led by the brothers Otto and Gregor Strasser, these "Strasserites" advocated for workers rights and mass action (ie using labor strikes and protests to push their agenda, a popular tactic among Socialists and Communists). However, they were never a large part of the party, and Nazi leaders like Hitler, Göring, and Goebbels were never part of the group. In summer 1934, Hitler had the Strasserite leaders murdered, and the rest of the Strasserites were imprisoned, or fell in line with Hitler's wing.
Cherry-picking issues to "prove" that Nazis were leftist. What I mean is, people will ignore the major issues (see the list above) and focus on relatively minor issues to "prove" that Nazis were leftist. For example, Hitler was famously a vegetarian towards the end of his life- and some people will actually try to use this as proof that he was a leftist! Or they'll point to the fact that Germany had universal healthcare during the Nazi era. While this is true, it's not that simple. First and foremost, universal healthcare was installed in Germany by Otto von Bismarck in the 1880s, before Hitler was even born! Second, the reason why Bismarck started it was because he hated socialism, and he basically hoped to kill its popularity by giving the people some of the things the socialists had been promising. Lastly, the Nazis expanded their healthcare system a bit, but this was primarily for racist reasons (to keep the races they liked healthy, and even to kill off people with genetic defects/disorders).
Focus on the "big government" issue. For some reason a lot of people, Americans in particular, believe that a country with a large government means that that government is alwaysleftist. This is ludicrous, and far from the truth. First off- what constitutes a "big government"? It's an arbitrary term. Furthermore, Nazis and Fascists are the prime example of right-wing movements that advocated large governments. Additionally, most anarchist movements are considered far-left, yet they advocate having no government at all. The size of the government isn't what makes it leftist or rightist; what that government does is.

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