In itself it would not be too bad, this is how we learn how things work, but add a media looking for sensation and political interests and this whole area of research becomes as scientific as astrology.
The physical basis of the theory is easy to understand, and was discovered in the 19th century: the atmosphere is obviously a heat reservoir, so what is trapping the heat? The answer is that certain atmospheric gases absorb and re-emit infrared light.
The obvious hypothesis is that if you increase the amount of those atmospheric gases, you'll trap more heat--just like building a taller dam will trap more water in a reservoir. This hypothesis was first proposed at the end of the 19th century. And today, that is indeed what a wide variety of measurements are showing: the gases are going up, and so is the temperature.
The hard part is predicting what exactly will change in a given location. Will New York get warmer or colder? Will Seattle get drier or wetter? Will Tokyo see more of the same storms, or fewer stronger storms? These are the questions that computerized GCMs will help us answer.
But we know that something is going to change. You can't dump more energy into a complex system (the climate, in this case) and expect it to keep working exactly the same way.