© 2015, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.