Doing science. Thing is, unlike what everybody likes to pretend, doing science means to do a lot of tedious hard work and not a whole lot of quick explanations. So the thing is, that we understand the physics of dilute gasses at roughly room temperature phenomenally well, we did all the experiments of putting this gas into a piston, and then heating the piston slightly, and then do it with a slightly different gas mixture, and then we double checked all these experiments and finally we got a pretty good theory sometime around the turn of the 19th century. Then you start to integrate all that knowledge with a knowledge of radiation basis, and you start doing cross checks and try to understand weather, and at some point try to start forecasting wether, with all the associated trouble and that was then sometime in the let's say 1960ies or thereabouts. (During WWII the flying wing of the US Army had meteorologists at all airfields, I believe German news started to broadcast weather forecast in the late 60ies.) Then you do all that with bigger computers and quite a bit of theory of partial differential equations, and then you realize that understanding the 11 year average is a much much better defined problem than next weeks weather. And all of these steps do suggest different cross checks. (Actually in the Physical Science Basis part of the 5th IPCC report there is a chapter called Evaluation of Climate Models ([0], p. 741), which goes into quite a bit of detail on the most recent efforts along those lines.)
[0] AR5: https://www.ipcc.ch/report/ar5/wg1/