This was explained to my class in great detail, as our teacher wanted us to make up our own mind as to who was more important in the discovery.
We all agreed that Rosalind Franklin was the most important person in the discovery of the DNA structure.
It was a conjoint effort, as zingerburger said, Rosalind Franklin had the diffraction patterns, which she got using xRay crystolography - BUT she also already knew the double helix structure, because the diffraction patterns she had were a feature of a helix structure.
Watson/Crick didn't discover the helix structure, they just made a model of it.
The movie we watched in class showed notes Franklin had written, with small sketches, which told how it had a double helix structure. Pretty much the only thing that Franklin didn't do was share her information willingly or make a model.
And then Franklin's lab partener [with whom she wasnt on good terms with] Maurice Wilkins, stole the pictures she had and gave them to watson/crick. They then made a model of what they thought was the DNA structure. They then took it to Franklin, and without her knowing that they had her picture, asked her if it was correct. She basically laughed at them.
What they had was an inside out model of DNA. They had put the bases on the outside. They then went back and changed it, and brought it back to her again... This time they were right. Then THEY got the nobel prize and didn't give her and credit for it.
Some time later, however, Watson wrote a journal/paper thing on his and Crick's discovery of the DNA structure, and made Franklin out to be a mean, self centered, unintelligent female. Crick then came forward and told the truth - and Wilkins backed him up. And that's how it all came to be.
And, there's some rule to do with not being able to take nobel prizes away [or so I hear], and not being able to give dead people nobel prizes [thus Franklin's work still goes somewhat unnoticed.]
Anyhow, that's how it was explained to me, and that's how I interpreted it. =)