How Do Greenhouse Gases Work?

I have no idea.  I googled and googled, and the best I can come up with is this page on Greehouse Effect Gases.

Still, no data on why CO2 absorbs more heat than say Nitrogen, or Oxygen.  What is the science behind   Someone please tell me where I can find this data and experiment setup.  There has to be solid science explaining this phenomenon since Greenhouse Gas is such a common phrase (over 14 million hits for a search of Greenhouse Gas on Google today).

The best thing I can find is that CO2 absorbs light in 3 frequencies... 2.7, 4.3 and 15 micrometers.  This seem like it is very very small, so given a large range of frequencies of radiation, how does increasing the concentration of CO2 from 320 to 390 ppm cause any variance of temperature?  First, 390 ppm is 0.039%.  An increase from 0.032% to 0.039% is a difference of 0.007%.  In that range of concentration of CO2, the temperature changed +0.4 degrees Celsius.  That means according to the concentraion of CO2 changed, the estimated CO2 cause of change should be between 0.036 and 0.104 degrees Centigrade.  The actual change in concentration of CO2 should have caused a 0.020 change in degrees Centigrade.  The math isn't adding up.

CO2 must be a byproduct of an increase in temperature, as I stated here in CO2 and Temperature.