A lot of the basic principles behind climate science are well-established physics and chemistry that have been known for over a century:
- Burning carbon compounds gives CO2
- CO2 captures heat
- More heat causes higher temperatures
The first step is basic chemistry, and has been abundantly supported by direct CO2 measurements in the atmosphere. The second step is directly reproducible in a laboratory environment, and its effect is used on an industrial scale in greenhouses. The third step is an immediate consequence of a thermodynamic law.
There is plenty of room for debate as to where the heat is absorbed, because the behaviour of the oceans in particular is fairly tricky, but apart from that these steps are beyond reasonable dispute. People disputing these three steps deserve the same warm welcome as inventors of Perpetual Motion devices.
Again, beyond these three basic points there is room for reasonable debate, but on a grand scale that doesn't really matter. More heat means higher temperatures somewhere and this will have consequences for ice and snow, for ocean circulations, for biotopes, and for the weather patterns. The `only' thing left is to establish exactly what these consequences will be on a smaller scale. And yes, that is tricky and requires more and more refined climate models. But that the climate is changing in some way is beyond reasonable dispute.