It'd require Haibara to buy a really old computer on the internet or perhaps at a yard sale, with all the accompanying equipment, so that she can access the data on the
assuming that Dr. Agasa doesn't already have that lying around the house somewhere. Also, they'd need a person knowledgeable enough in programming to remove Night Baron from it.
Alternately, assuming that the Organization keeps its info on a cloud server or whatnot nowadays, all they'd need to do is steal Gin's, Vermouth's, or Rum's computer or phone and figure out the password/PIN. Alternately, the data might be stored on a flash drive, in which case they'd need to get their hands on that and figure out how to bypass the encryption/virus software that it'd inevitably have.
After this was done, Haibara would need to be hidden and guarded carefully for the next few months so that nothing happened to her while she worked on developing the cure, since getting her hands on this data in the first place would likely alert the Organization to the fact that she's still alive.