How in the heck have you figured out the weather patterns so well? That part's always my worst enemy!
It’s a step-by-step process and everything builds upon few but important foundations. Those are the basic properties of the planet (position within the habitable zone of its parent star, planetary size, axial tilt), shapes and sizes of the continents (including plate tectonics which drive orogeny), the composition and density of the atmosphere and the rotational direction and speed of the planet. The rotation dictates the general direction of the main winds, the axial tilt influences the ITCZand the pressure system it maintains, mountains block clouds and modify rain patterns, the distribution of land and sea dictates oceanic currents and their influence on global climate, and so on. It’s quite a bit to read and to learn, but it all comes together after a while and as soon as it “clicks”, it’s easy to understand.
From then on, it’s diligent but routine piece of work. I started with the base map of the continents, then added the ITCZ based on my data, then built the pressure system upon that, derived the rain patterns from the combination of atmospheric pressures and land/sea distribution, derived temperature from illumination angles and altitudes, and then mixed everything together to deduct the climate classification that’s used on Earth.
You have to want to understand and like the topic, though. If you find it interesting, yet intimidating, I really recommend watching student videos on those topics on YouTube. They explain everything well, and you get a good overview over the basics before diving into the meat of the topic. Does this help you further? :)