In the 90s I got interested in climate change induced by burning fossil fuels and participated in sci.environment discussions about it. Here is my layman's take.
Simple models predict that increasing the concentration of CO2 in the atmosphere will cause the average temperature at the surface to increase. Burning fossil fuels adds CO2 to the atmosphere and measurements show that in the short term about half of it remains there increasing the concentration of CO2 in the atmosphere. Observations also show that the earth's surface has been warming. The amount of the warming is roughly consistent with the amount predicted by simple models. So it is plausible that burning fossil fuels has warmed the earth and will continue to do so.
There is some room for doubt as the simple models leave out a lot of things and more complicated models are difficult to validate. So detailed predictions are quite untrustworthy. Still there are real reasons for concern even if it is not absolutely certain that major problems will result.
So what can be done? It appears that in the long run the impact will mostly depend on how much of the world's supply of fossil fuels gets burned. Within limits the rate of burning doesn't matter too much. So conservation doesn't help much if it just delays the time it takes to exhaust the earth's supply of fossil fuel. Some fossil fuel has to be left in the ground.
The three main fossil fuels are oil, natural gas and coal. The oil will run out first, followed by the natural gas and finally the coal. I see little chance that all the oil and natural gas won't get burned. There is some chance that we won't burn all the coal. Currently coal is mainly burned to generate electricity and there are alternative ways such as nuclear power to generate electricity. They are more expensive but not impossibly so if limiting climate change becomes imperative.
A key turning point will occur when the oil runs out. It is technically feasible to make oil from coal. Currently oil from coal is not cost competitive but this will change as the oil runs out. If this leads to large scale conversion of coal to oil it seems inevitable that all the coal will be eventually burned. In which case we best hope the climate effects are not too costly or that some sort of active mitigation is feasible.