Mathematics and measurement for starters. And accurately reporting what the evidence consists of.
Sure, there is more to it than that, and sure, some studies are qualitative rather than quantitative, but if your theory requires one plus one to equal three, or error bars of just ±5% to justify a claim that hundreds of thousands of other measurements are all consistently out by six orders of magnitude, or rock formations to be not fractured when in reality they are, then your theory is wrong.
I think you’re missing the point here. Yes, intuition has its place, but the point is that some scientific discoveries fly in the face of what you would expect from “common sense” and intuition alone. Look at quantum mechanics for starters. Or the fact that more entropy means more information – which is the exact opposite of what most people who have never studied the subject properly expect.
In fact this is the exact point that Darwin was trying to make when he described the evolution of the eye as “absurd in the highest possible degree.” He was making the point that common sense and intuition are not a reliable guide to what is “absurd in the highest possible degree” and what isn’t.
When it was first said that the sun stood still and the world turned round, the common sense of mankind declared the doctrine false; but the old saying of Vox populi, vox Dei , as every philosopher knows, cannot be trusted in science.