Making future predictions…
Basically get the biggest computer you can lay your hands on, account for as many variables as possible that are involved in climate feedback, such as solar variations, ice and snow albedo, water vapor and other blanket gases, ocean and land carbon sinks (use known equations or develop new ones and stick to basic laws of physics energy conservation, mass and momentum), set the computer off and hey presto, three months later, many millions of calculations later, there is your climate model for the next 250 years. Simples!
Yes all this from the person who struggles with basic IT, never mind basic physics and maths.
However the people that are developing these complex models have tested them against what we do know from observable historic data, and conclude they are capable of projecting (not predicting) future patterns. Big difficulty is knowing precisely what is gong to happen with future CO2 emissions. (Human activity and our CO2 is the new kid on the climate systems block) Will we continue with our growth at all cost, business as usual behaviour? Or will we get our shit together and create a sustainable future? Conservative models find scenarios where we manage the latter will take us to 2° temperature increase, still with extreme weather patterns but more chance of planetary feedback loops staying in balance. Business as usual scenarios can take us to 6° warming, not very brilliant at all, and into tipping point territory. All hell breaks loose for whatever humanity is left and the rest of the biosphere.