Dill demonstrates his idolization for the Finch family very personally for each member.
First, Dill seeks to be found suitable by Jem throughout the story. Early in the book, he earns Jem's approval by sharing about having seen the picture show Dracula and by knowing so many stories.
Later, Dill shows his affection for Scout by proposing just like children would propose. This gives Scout hope for their future together and helps her know what extents he would go to in order to maintain their friendship.
Dill runs away and sneaks into their house. He hides under Scout's bed. In fact, before he even goes to Miss Rachel's house, he tries to stay with the Finch family. This shows respect for Atticus as a parent, but even greater affection for Scout and Jem as sibling figures. Dill's life has been a variety of lies to the kids. When he ran away (it is hard to know the details in between what could be Dill's lies), Dill chose a family to trust, and that was the Finch family.
Dill saw all parts of this family (good and bad) and loved being with them anyway. Dill saw Atticus that night at the jail. Dill got in trouble with the kids for playing "strip poker" and the Boo Radley game. Dill got to experience the trial and watched Atticus fight for what was right. Although the novel doesn't directly state that Dill idolized him, we certainly see Dill experience Atticus as a man of conviction, discipline, and integrity.