Graphical techniques standing from well-known theory of angular momenta
coupling, are developed to provide an improved understanding of the addition of two angular momenta. Such methods are used to find, when j1 and j2 being given, which are the values of the total angular momentum J that are carried out, how much of distinct subspaces are associated to each, and how the eigenvectors of J2 and Jz be developed on the product basis in terms of Clebsch-Gordan coefficients. A practical evaluation of Clebsch-Gordan coefficients is also given. Concrete examples are given for this general method.
