The basis of Grothendieck's esquisse d'un programme is that there exists an action of the absolute galois group of the rationals on the Teichmuller tower, the collection of all etale fundamental groups of the moduli spaces of algebraic curves. Not only this, but apparently Belyi's theorem can be used to prove that it is already faithful on $\pi_1^{et}(\mathcal{M}_{0,4})$.
I've looked at quite a few resources discussing this and none of them actually explicitly define what this action is (or what it is induced by). Are there any resources that explicitly define the action and give a proof using Belyi's theorem that this action is faithful?
Thanks for any help.