The Sphere Grid becomes accessible after Rikku explains how to use it in a short tutorial. Each character who joins the party has a pre-designated starting point on the grid. While each of the characters has his or her own section, you can remove the locks between the different sections by using the appropriate key sphere.
Thus, character advancement is limitless. While in the Sphere Grid, press the Select button to zoom out from the current character’s position to see his or her relation the other characters. Press and to change the viewing angle of the grid you desire.