This paper describes and illustrates the use of Adpositional Argumentation (AdArg), a new formal method that enables the analyst of argumentative discourse to represent linguistic and pragmatic information in a highly detailed and yet flexible way. It first explains the theoretical starting points of the method, which is a combination of the linguistic representation framework of Constructive Adpositional Grammars (CxAdGrams) and the argument classification framework of the Periodic Table of Arguments (PTA). It then lays out the basic steps of the method and illustrates them by explaining how to build a so-called 'argumentative adpositional tree' (arg-adtree) of a concrete example of an argument.