Listen (and read) closely. See if there are any emotional appeals in the speech or text you are listening to or reading. These are appeals to pathos and can (and often do) undermine an argument. Try to look for appeals to logic and facts backed by research, experimentation, data collection and analysis, and projections made by experts in the field about the history and future of a topic.
Fact check. Research the claims being made. Who made them? Weigh facts more heavily than opinions: if a group of scientists with thousands of research hours between them tells you something, you might want to consider this claim to be more probable and logical than the claim made by a lone journalist who was expressing an opinion as opposed to the result of empirical evidence, data analysis, and critical examination.
If you can, trace the source back as far as you can, from newspaper articles on the subject to the original research paper or place where this claim was first made. Who funded that research? If, for example, a company or NGO with vested interests in one outcome over another funded the research, be wary. Data can be skewed, and often confirmation bias is often a dangerous thing - if one is looking to prove a claim, one might ignore contrasting data or data that does not agree with a prefabricated conclusion, or one may understate the importance of this outlying data.
Try to put the argument in your own words. If you cannot sum it up, chances are you don't quite understand it well enough to make a determination of its veracity. If you can summarize it, see if it makes logical sense. Try to determine the potential biases of the source, and the source behind that. Many times, when you read the news, you see a sort of filtering-down of information. It's almost like a game of telephone. A research paper is published in an academic journal, and then a fraction of it is used and perhaps sensationalized or quoted out of context in an article that merely skims the very surface of the original research paper.
If you can find an academic paper on a topic you are unsure whether or not it's a fact or an exaggeration masquerading as the truth - do so. Learn as much as you can, because the more you learn, the easier it is to discern weak arguments from strong ones and true statements from false ones bolstered by rhetoric.
