The Nationalists blamed the bombing on the Republicans, saying that Republican forces destroyed the town. There was precedent for this, as the Republicans set fire to the town of Irún in August-September of 1936. They also used dynamite to destroy key installations to deny their use to the Nationalists. So the Nationalist narrative of the Republicans destroying a town had precedent when Guernica was aflame in April of 1937. This story was a complete fabrication. The German Condor Legion had attacked the town on behalf of the Nationalists. This was correctly reported by George Steer, who found a wide readership. He also reported on bomb fragments with German markings that proved who the authors of the attack truly were. (You can read more about Steer in a number of places, including Paul Preston's We Saw Spain Die. Foreign Correspondents in the Spanish Civil War)

Paul Preston gives the response of a German officer asked about the bombing as follows:

We bombed it and bombed it and bombed it, and bueno, why not? (Paul Preston, The Spanish Civil War, 270)

He also says that the reporter was urged not to print that quote (and censorship of the press was common in Nationalist Spain). The Germans were technically following a policy of non-intervention, and I cannot recall reading of any comment by the German nation on the subject. Of course, the reality was that the Luftwaffe's involvement was an open secret. The Nationalist claim of Republican involvement was a smokescreen, and some foreign and domestic people bought the story--mostly people that were already supporting the Nationalists.

Preston's The Spanish Civil War has a good overview of Guernica, and he has a small book on the subject as well. Beevor's book covers the military side of the situation in a bit more depth. There are also a number of other books specifically about Guernica, as well as Picasso's painting by the same name.