I’m not a protein crystallographer, but here’s my generalist take.
We understand the physics of e.g. X-ray diffraction pretty well, so we can fit pretty decent forward models for the x-ray data given a proposed structure. The hardest task here is getting a good enough guess at the structure to optimize the physical model, and it’s my impression that people use an iterative model refinement workflow. At least that’s how it’s done in condensed matter materials.
There are many sources of experimental uncertainty, like the non-ideal nature of the x-ray source and optics, and the fact that the atoms in the protein are not static but have some thermal fluctuations. so at the end of the refinement you still have some uncertainty on your model parameters (the interatomic distances for proteins I guess), but if you are careful you can calibrate these uncertainties pretty well.
X-ray diffraction is pretty nutty, too. You're taking the diffraction pattern, which is the fourier transform of the electron density. Fourier transform results are complex-valued data. Unfortunately, we don't really have X-Ray lasers, so you can only get the intensities and not the phases of those diffraction spots. Since mother science hates us, it of course the case that, in a fourier transform "more information" is contained in the phases than in the intensities.
So you "make guesses at what the phases are", the best choice is to bootstrapping these phases measured with another technique (you can introduce crystal defects that do allow you to guess at what the phases are).
Less scrupulous is to use a computer generated model, like fitting another protein "that you guess is related", then you model the electron density, take the phases of that.
In any case you take these "phase" guesses, and then apply it to your intensities, re-run the fourier transform, refine your electron densities, twiddle the location where you think the atoms, are, then repeat with your new model. This process repeats until you converge on a structure that you're happy with.
Now alarm bells should be screaming in your head right now: Yes, it's entirely possible to converge on a wrong structure, especially if you're a young up-and-comer professor seeking tenure that has no ethical problems with "suggesting" their grad students to sleep in the lab and work 100 hour weeks and willing to do slipshod work to get you tenure: https://www.sciencedirect.com/science/article/pii/S002228360...
Best is an orthogonal process (like NMR). Cryo-EM is getting better too so maybe that will start to be viable. Sometimes that's not possible, but you can use secondary evidence: "we know these three amino acids are important band hey look they touch in our model".
