Just to clarify, the helical structure (or "Watson-Crick" structure) of DNA wasn't discovered using x-ray crystallography (as Dr. Novella mentioned), but x-ray diffraction. The DNA was in solution, and not crystallized.
X-ray crystallography is x-ray diffraction photography performed on crystallized substances (typically purified proteins). Getting proteins to crystallize is an entire art in itself. Interpreting the x-ray diffraction pattern into an 3D electron density map is another art. Then fitting a chain of amino-acids (essentially a protein) into that 3D density map is another art in itself.
Edit: I could be wrong about it not being crystallized. That's what I recall from my structural class 10 years ago. It's not clear in the original, extremely short 1953 paper (no Materials and Methods).