The plot of A New Hope revolves around the Death Star technical plans, which Princess Leia gives to R2-D2.
How did she and the rebels get hold of the plans?
The short answer is that we don't know (yet). The mission to steal the plans will apparently be a major part of the new Star Wars spin-off film; Rogue One.
"Edwards revealed that the film will revolve around a rogue band of resistance fighters who unite for a daring mission to steal the Death Star plans and bring new hope to the galaxy. “I couldn’t sit in a cinema and know that someone else made this film,” Edwards said in the panel. Fans were treated to concept art and a brief video that caused a packed house to erupt."
As for the EU version(s) of events, this has now been completely disregarded. Pablo Hidalgo famously quipped;
"...if you had to throw a dinner party and invite everyone who had ever stolen the Death Star plans, you'd be surprised at how many place settings you'd have to worry about."