Here is what you would find out if you read any introductory college textbook on climatology:
Climate is what we call the long term pattern of prevailing atmospheric conditions. Weather is what happens daily. Climate is the long term average of weather, locally and globally,over periods of decades centuries, millenia, and longer. Weather is about 66% predictable with present knowledge, models, and computers. Because it involves averages over long periods, climate is much more predictable than weather, better than 90%.
Various means can be used to find out what the average CO2 concentration of the atmosphere has been over the past hundreds, thousands, and even millions of years. Various other means can be used to find out what the average earth surface temperature was, what the average rainfall was, what the mean sea level was, and what the frequency and violence of tropical storms was.
About 1900, it was noticed by climatologists that the average earth surface temperatures appeared to have been increasing since about 1750. By then, they knew that there were fluctuations in average temperatures over periods of decades, centuries, millenia, and longer periods. At that time, they did not know which variations were due to which causes, nor did they know all the possible causes for such variations. A Nobel Prize winning chemist, an expert in thermodynamics, by the name of Svante Arrhenius, proposed that substantial increases in atmospheric carbon dioxide concentrations had the potential to cause substantial increases in atmospheric temperatures.
As of now, climatologists know exactly what variations have occurred in average earth surface temperatures over long and short periods of time. They know precisely how much variation is due to each of the potential causes of solar output variation, earth orbital variation, earth axial rotation variation, atmospheric gas concentrations, and other effects. Each of the cycles has a name, usually in honor of some climatologist instrumental in figuring it out.
We now have figures and calculations that show, with greater than 90% certainty, the following:
1) average earth surface temperatures have risen about one degree centigrade since 1750 over prior long term averages;
2) the concentration of CO2 in the lower atmosphere has about doubled since 1750 over prior long term averages;
3) the CO2 change accounts for almost all the temperature change, and there is almost no variation left unaccounted for.
Given that the causal mechanism makes sense, and that the math is highly certain, the conclusion is beyond doubt - earth's climate is getting warmer due to increased CO2 in the air. It is also very highly likely that the increased CO2 concentration is almost entirely due to the combustion of fossil fuels.
Now, what are you going to do about it?