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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 What are dessins d'enfants?, especially notice Leila Schneps - Dessins d'enfants on the Riemann Sphere.