One detailed presentation of the ADM formalism may be found here: http://wwwteor.mi.infn.it/~molinari/TESI/Danieli_tesi.pdf; another is here: http://philsci-archive.pitt.edu/11446/1/Giulini.pdf

but, by itself, the formalism doesn't have anything to do with loop quantum gravity.

The ADM formalism is classical.

How to recover general relativity from loop quantum gravity is, still, an open problem.

A review of the issues involving the constraints may be found here: Article Critical Overview of Loops and Foams

Thank you Stam Nicolis

You’re most welcome, Rakshit Prafulkumar Vyas