The early 20th century American social critic and humorist H. L. Mencken, known for his "definitions" of terms, defined a demagogue as "one who will preach doctrines he knows to be untrue to men he knows to be idiots."
As George Bernard Shaw said: "But though there is no difference in this respect between the best demagogue and the worst, both of them having to present their cases equally in terms of melodrama, there is all the difference in the world between the statesman who is humbugging the people into allowing him to do the will of God, in whatever disguise it may come to him, and one who is humbugging them into furthering his personal ambition and the commercial interests of the plutocrats who own the newspapers and support him on reciprocal terms."
Max Weber: "Political leadership in the form of the free 'demagogue' who grew from the soil of the city state is of greater concern to us; like the city state, the demagogue is peculiar to the Occident and especially to Mediterranean culture. Furthermore, political leadership in the form of the parliamentary 'party leader' has grown on the soil of the constitutional state, which is also indigenous only to the Occident."
Though this definition emphasizes the use of lying and falsehoods, skilled demagogues often need to use only special emphasis by which an uncritical listener will be led to draw the desired conclusion themselves. Moreover, a demagogue may well believe his or her own arguments (for example, there are good reasons to assume that Adolf Hitler - certainly one of the most successful demagogues in history - sincerely believed his own anti-Jewish diatribes.)
A famous usage was by the aging Erich Ludendorff, who was for a time a strong supporter of the early rise of Adolf Hitler and Nazi Germany. After learning of Hitler's appointment as Chancellor, he expressed his disappointment to German President Paul von Hindenburg :
Hitler indeed would become regarded as perhaps the epitome of a demagogue, having successfully risen to power through appeals to the ethnic and nationalistic prejudices and vanities of the German people.
Apples and oranges — mixing of incomparable quantities. For example, "our government has increased social spending by 5 billion dollars, while the previous government increased it only by 0.4 percent." The latter sounds like less, but one cannot be sure without an absolute value.
Half-truth — making statements that are true only in a strict and relatively meaningless sense. For example, "the opposition have accused us of cutting foreign aid, but actually our government has increased foreign aid by 500 million dollars," not mentioning that (adjusted for inflation) the allocated funds have in fact gone down.
False authority — relying on the general authority of a person who is not proficient in the discussed topic. For example, "the professor read my book, and liked it very much," omitting the fact that it was a professor of chemistry who read a book on anthropology.
False dilemma — assuming that there are only two possible opinions on a given topic. For example, "You're either with us or against us...," ignoring the possibility of a neutral position or divergence.
Demonization — identifying others as a mortal threat. Often this involves scapegoating — blaming others for one's own problems. This is often advanced by using vague terms to identify the opposition group and then stereotyping that group. This allows the demagogue to exaggerate this group's influence and ascribe any trait to them by identifying that trait in any individual in the group. This method can be aided by constructing a false dilemma that portrays opposition groups as having a value system that is the polar opposite of one's own, as opposed to simply having different priorities. This method was incorporated by the Nazi regime to gain the general support of the public when it began to initiate its anti-Semitic policies.
Straw man — mischaracterizing the opposing position and then arguing against the mischaracterization.
Loaded question — posing a question with an implied position that the opponent does not have, e.g. "When did you stop taking bribes?"
Unrelated facts — bringing unrelated facts that sound in favor of the speaker's agenda. For example, marking a vegetable or cereal product as "cholesterol free". Since cholesterol is only found in animal products, such labeling does not actually distinguish this product from similar competitors.
Emotional appeal or personal attack — attempting to bring a discussion to an emotional level. For example, "Everyone is against me!", "Can't I be right just once?", "You're stupid!", or just the classic retort "Shut up!"