Boo Radley was always a good man--it's Scout and Jem's perception of him that changes. At first, Jem receives all his information about Boo Radley from Miss Stephanie Crawford, which is a mix of fact, error, and gossip. Boo had done a little joy-riding in his youth with a bad crowd once, but that doesn't make him a bad man. Nevertheless, Miss Crawford helps to shape their perception of Boo Radley as a spooky phantom or boogieman who lives in a haunted house a few doors down from them. As the children learn more about him and try to get closer to him, though, they discover that he's always been nice--it's just the rumors that painted him as bad.
First, in chapter 4 the children discover gum and two Indian-head pennies in a knot-hole of one of the Radley's oak trees. It isn't until chapter 7 after the kids receive two carved soaps of themselves, a spelling medal, and a pocket watch with a knife on it that Jem starts truly thinking that Boo Radley might be the one sending these gifts to them. He suggests to Scout that they write to whomever is doing this a thank you note. It's at this point that Jem almost reveals that he believes that Arthur (Boo) Radley is the kind man giving them things.
"He had been on the verge of telling me something all evening; his face would brighten and he would lean toward me, then he would change his mind. 'Here, let's write a letter.' I pushed a tablet and pencil under his nose.
'Okay. Dear Mister. . .'
'How do you know it's a man? I bet it's Miss Maudie--'
'Ar-r, Miss Maudie can't chew gum--' Jem broke into a grin" (61).
By saying "Ar-r," Jem almost reveals that he believes Arthur (Boo) is the kind gift giver, not a bad man.
In between the times that the kids receive the first and second sets of gifts, Jem creeps up to the Radley's back porch on the last night of summer with Dill and Scout looking on. In chapter 6, Jem wants to get a peek at Boo from a back window, but Mr. Nathan Radley comes out and shoots a gun in the air; so, the children run for their lives. Unfortunately, while scrambling under the fence, Jem's pants get stuck in it. He leaves them there in order to escape, but goes back for them later that night. In chapter 7, he reveals to Scout what happened when he went back for his pants:
"When I went back, they were folded across the fence. . . like they were expectin' me. . . And something else. . . They'd been sewed up. Not like a lady sewed 'em, like sometin' I'd try to do. All crooked" (58).
Jem says the above quote in between discovering the first set of gifts in the knot-hole and the second set in chapter 7. This experience helps him to start to believe that Boo Radley is a friend and not an enemy. The fact that Boo Radley is a good man is finally settled in Jem's mind on the night that Miss Maudie's house burns down in chapter 8.
On the night of the fire, Atticus has the kids stand out front of the Radley's house so he can keep an eye on them during rescue efforts. When they get home that night, Atticus asks Scout where she got that blanket around her shoulders. Jem realizes that it must have been Boo who draped it around her during the fire. Then he spills all of his experiences and deductive reasoning on Atticus to show that he believes Boo Radley is a good man, not a bad one:
"Jem seemed to have lost his mind. He began pouring out our secrets right and left in total disregard for my safety if not for his own, omitting nothing, knot-hole, pants and all. . . 'I sweart to god he ain't ever harmed us, he ain't ever hurt us, he coulda cut my throat from ear to ear that night but he tried to men d my pants instead. . . he ain't ever hurt us, Atticus--'" (72).
The above quotes show how Jem's perception of Boo Radley progressively changes. Again, Boo was the same before Jem thought he was bad, but Boo was the same the whole time. Jem and Scout just needed to get to know him first in order to realize that he is good. The lessons to be learned are not to listen to gossip and get to know someone first before passing negative judgment.