What would be the defining characteristic of New-Keynsian thought? If you had to summarize New-Keynsian thought into one paragraph, or a set of equations, what would it be?
Gali's Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework, provides an advanced undergraduate / first-year graduate student introduction to these models, and I'd recommend it for self studies. According to chapter 1, available online, which offers an overview of the  New Keynesian Model, the key elements are:


Structural characteristics of Real Business Cycle (RBC) Dynamic Stochastic General Equilibrium (DSGE) models
Monopolistic competition
Nominal rigidities
Short run non-neutrality of monetary policy