There are three levels in the atmosphere where CO2 could act: at the surface, in the troposphere, and high in the atmosphere where radiation to space is greater than thermal absorption. In each location the conditions are different, and the way CO2 acts is different.
At the surface, the CO2 “back radiation” has been a mystery to many, this author included. Some argue that such a thing doesn’t exist, that it is against the second law of thermodynamics. It does exist, but the mechanism does not work very often, or exactly as advertised. This article will throw you some curves, and many numbers, but will stay away from complicated mathematics. Complex math is unnecessary.
First, the basics: CO2 is a three-atom molecule. It can be visualized as one carbon atom with two oxygen atoms attached, one on each side, in a straight rod configuration. As such, it is “non-polarized”, that is the charges on each atom balance, and the charge on the whole molecule appears to be zero as viewed from any angle. Thus, it has only two modes of vibration when excited by infrared radiation (IR). It can vibrate in and out along the long axis, like a rod that has been struck on one end, or it can vibrate parallel to the axis, like a rod that has been struck in the middle.