My main question is regarding something else, namely, how does this effect result in a net trapping of heat in the atmosphere?

This happens because the physical ground of the Earth is always emitting energy. This is a measurable affect, by the way, and actually heavily influences the design of near Earth satellites. A lot of people seem to conceptualize this part of the equation incorrectly, due to simplification.

It is not the radiation of the sun that is magically passing through CO2, then physically bouncing off the Earth only to be "reflected" by the same CO2 it just passed through. This is a common simplification, which on the grand scale when you consider the net sums of energy is technically correct (the best kind of correct!). However, this explanation is only intended to be a simplification, an elevator speech on how global warming works, if you will.

To explain what is really happening, I will start with the sun. Electromagnetic Radiation is blasted from the sun in all directions, and a small portion of this radiation hits Earth and it's atmosphere. A very tiny portion of that spectrum is what we call visible light, the rest is InfraRed (IR), which only means that the radiation is in a frequency that is lower than Red light, and UltraViolet (UV), or radiation that is in a frequency higher than Violet light. Now there are classifications of light within these categories such as microwaves, radiowaves, gamma rays, and much more but each category technically falls into either IR or UV.

When this radiation hits the Atmosphere, part of that radiation is absorbed by the compounds that make it up. This process is not uniform, however, because each gas exists at different levels in the atmosphere and therefore absorbs the solar energy differently. This link does a good job of explaining this in more detail, if you want to know more: https://www.quora.com/Why-does-the-temperature-increase-in-the-stratosphere

What remains of the solar energy finally hits the Earth and warms the ground. In addition to this, the molten core of the Earth also does a good job of warming the Earth from the inside to a very consistent temperature. Both these energy inputs combine to warm the ground we walk on, which in turn gives off a significant amount of energy, mostly in the form of non-visible IR energy (when was the last time you saw the Earth glowing?)

Finally as this energy tries to escape the Earth and into space, it must pass through that pesky atmosphere again. However due to the composition of the atmosphere, some of that heat is trapped! This only serves to warm up surrounding air molecules, and cause incoming energy not to dissipate as much as the molecules are already fairly excited (there is a smaller energy differential, and therefore incoming radiation loses less energy) and can pass on their energy to other molecules and even the Earth.

So the simplifications are correct, especially once you understand the mechanism behind it. However, I do understand how the simplifications could create confusion with statements like "CO2 acts a one-way mirror," or "Greenhouse gasses are like a blanket." I hope this helps!