A First Course in Loop Quantum Gravity by Gambini and Pullin sounds like what you were looking for, but the following articles and papers may also be relevant. These are roughly in increasing order of length and difficulty.
Smolin, "Atoms of Space and Time," Scientific American, Jan 2004 (the PDF is easy to find on the web by googling)
Baez, slides from a talk titled "Spin Networks, Spin Foams, and Quantum Gravity," http://math.ucr.edu/home/baez/foam/
Carlo Rovelli, Peush Upadhya, "Loop quantum gravity and quanta of space: a primer," 1998, http://arxiv.org/abs/gr-qc/9806079
Rovelli, 2010, "Simple model for quantum general relativity from loop quantum gravity" -- http://arxiv.org/abs/1010.1939
Rovelli, 2010, “Loop quantum gravity: the first twenty-five years,” http://arxiv.org/abs/1012.4707
Rovelli, 2011, "Zakopane lectures on loop gravity" -- http://arxiv.org/abs/1102.3660
This post imported from StackExchange Physics at 2014-03-17 03:42 (UCT), posted by SE-user Ben Crowell