Daisy and Nick are cousins. The two do not know each other well as the novel opens but they re-connect in the early chapters of the narrative. Tom, as you know, is Daisy's husband when the action of the novel begins. He and Nick know one another from college (Yale), where Nick developed a negative impression of Tom.
"Daisy was my second cousin once removed, and I'd known in college. And just after the war I spent two days with them in Chicago."
The question of how these three characters relate quickly becomes complicated when Nick visits Daisy and Tom for dinner in the first chapter.
Daisy seems to want an audience to amuse herself and to demonstrate the various points of interest of her position. Being married to Tom, Daisy is rich and, according to her, "sophisticated," but appears to be so bored that she has to concoct dramatic scenes.
The dinner party is just such a dramatic scene as Tom receives a phone call from his mistress during the meal. After witnessing the tension and hearing about Tom's affair, Nick reflects that his "own instinct was telephone immediately for the police."
When he leaves he is "confused and a little disgusted" despite the fact that he had felt a "stirring warmth" from Daisy at one point and had been very conscious of her charms.
As the story moves forward, Nick's feelings for both Daisy and Tom remain largely unchanged (complicated, distanced, and somewhat disdainful). He appreciates Daisy's charms and loathes Tom's ignorance and arrogance. He helps Daisy and facilitates her affair with Gatsby, but also helps Tom carry on his dalliance with Myrtle by staying silent about the affair.
Caught in the middle of a sordid set of relationships, Nick looks at Tom and Daisy as people of a different circle and status who use their position of privilege as moral insulation and as a mask for their personal failings.
"They were careless people, Tom and Daisy -- they smashed up things and creatures and then retreated back into their money or their vast carelessness [...]"