The word is originated from the older name of a congregation of the Roman Curia, Sacred Congregation for the Propagation of the Faith. Their simplified Latin name was Propaganda Fide. The congregation is responsible for missionary work and related activities. So the word had got a special meaning related to the work of the congregation, now it means a set of messages aimed at influencing large number of people.
You can find many resources about propaganda, how does it work and how it was used in past. You can also find a list of methods used. And I think that most of the methods use a limited number of cognitive biases to influence people. You can also check it yourself comparing the methods of propaganda to the list of cognitive biases. I founds these biases: halo effect, аvailability heuristic, illusory truth effect, illusory correlation, framing effect, attentional bias, Barnum (Forer) effect.
Fortunately these biases can be dealt with using similar approaches. You can look for more information and for alternative explanations and hypotheses, because for most of these biases to work your access to information should be limited. Or your processing of information should be limited, because people tend to save their mental resources, which leans to cognitive misery. According to K. Stanovich1 there are three main processes how it can happen. A person can default to autonomous mind and do not use higher cognition; a person can focus too much on something and do not move to other thoughts; a person fails to switch to higher cognitive functions when a situation requires. To avoid all these examples of cognitive misery you need to call to analytical and reflective minds more often, probably making a habit of it.
But there are ways to identify and fight propaganda even if you do not know which cognitive biases are used. Instead you can do two things, first you should look for a possible goal of a suspicious text. If the goal does not benefits you and if it is not obvious from the text, it could be a piece of propaganda. Next you should check the logic of the text and how it operates with facts. Propaganda often uses logical errors to create a false conclusion, so you can trace arguments from premises to final conclusions. And even if the logic looks good, the text can still cherry-pick facts and its use of induction logic will be wrong. It is harder to find because you most likely need to check other sources of information.
Still, some errors in induction logic can be noticed even without checking sources. For example if an argument uses a single evidence to draw a conclusion about the whole population, it can be a logical error. Consider this argument: a boy likes pizza; he kicked his brother today. Therefore boys who like pizza are more violent.
It may looks clearly incorrect due to not very realistic conclusion, but if a conclusion more realistic, an error like this would be harder to spot. But you can still start from examples like this, or you can get a real fact and try to create an incorrect argument that should give you a correct conclusion.
1. ^ : ME Toplak, RF West, KE Stanovich (2011). Intelligence and rationality. In The Cambridge handbook of intelligence
RJ Sternberg, SB Kaufman - 2011 (pp. 784-826).