The radiative forcing phenomenon consists in absorbing some of the long wave radiation emitted by the lukewarm surface of the Earth. Thus, that part does not exit the Earth directly and causes the atmosphere to slightly warm, up to a point where an equilibrium output=input is re-established.
Dumb deniers want to not believe this, they can cook in their own soup if they know how to heat it.
To get an understanding of the phenomena, the analogy of the greenhouse has been proposed.
But it is not telling the right story since it consists in keeping warm air in an enclosed space rather than to absorb and re-emit electromagnetic radiation.

I propose here a bathtub analogy: When water flows continuously into a bathtub it will overflow. To maintain the level constant, the discharge pipe at the bottom of the tub needs to be open. The water level will establish itself at the point where the water head (pressure) is high enough to cause the flow through the opening to be equal to the inflow. When the opening is too wide the tub will eventually remain empty. If the opening is too tight, the level will raise further, up to overflowing into the bathroom. Understood? Let's assume that the exact opening has been found, with which the height h will remain constant. Now comes a disturbance that we will call crumb: something restricts slightly the outflow (some call this hair lumps). The water level will rise until the pressure (proportional to the height h) is high enough to overcome the restriction. The crumb has forced up the water level.

In this analogy, matter is used instead of energy; but it is still one of these bathtub problems that have caused so many headaches to uninterested schoolchildren.

• The water inflow is the solar irradiation hitting the Earth
• The water outflow is the energy leaving the Earth in the form of direct reflection (ultraviolet, visible), or of radiation in the infrared range.
• The equilibrium is reached at a given water level, corresponding to the temperature of the atmosphere.
• The tub is neither empty nor is it overflowing. In and outflow must be equal.
  As we don't cook nor freeze totally, the entry and exit energy fluxes must be equal, regulated by albedo, clouds, and emissivity
• One of the crumbs is the absorption by so-called greenhouse gases of some of the irradiated energy.
  The more or the larger the crumbs in the outlet valve, the higher will be the water level.
  The higher the concentration of GHGs in the atmosphere, the higher will be the temperature.

No gain, no loss, no violation of any physical law.
The only questions causing the climate controversy are:

• how sensitive is the level to the amount and the size of crumbs?
• are all the crumbs caused by carbon?
• how many crumbs can be attributed to human activities?
• will reducing the production of human carbon crumbs help to significantly prevent the tub to overflow?