While there are a lot of ideas in the comments, I think the upshot is that if you want to read Deligne's monograph “Le Groupe Fondamental de la Droite Projective Moins Trois Points” (http://www.math.ias.edu/files/deligne/GaloisGroups.pdf) and are not working with someone who already understands it, then you need to look at the later literature on Dessins d'enfants.  Good references are given in https://mathoverflow.net/questions/1909/what-are-dessins-denfants, especially notice [Leila Schneps - Dessins d'enfants on the Riemann Sphere][1].


  [1]: http://people.math.jussieu.fr/~leila/Fschneps.pdf