Nearly everything Atticus says reflects his values and principles. I'll give you three of the most significant and common ones, and there will be plenty for others to add, I'm sure.
"You never really understand a person until you consider things from his point of view - until you climb into his skin and walk around in it."
This is indicative of Atticus's belief that everyone has a story and deserves respect just for living. He applies this philosophy to some pretty difficult circumstannces: Mayella in the courtroom, Mrs. Dubose as she's villifying both him and his children, the Cunninghams who come to cause trouble (or worse) at the jailhouse, and Bob Ewell spitting in his face. Atticus encourages his kids to follow this principle, and he lives it out in front of them every day.
"Mockingbirds don't do one thing but make music for us to enjoy... but sing their hearts out for us. That's why it's a sin to kill a mockingbird."
This is Atticus's figurative way of saying things that are innocent and harmless and just trying to be who God created them to be should be left alone to make whatever music they're called to make. In the course of this novel, several characters might qualify as mockingbirds; however, the two most obvious are Boo Radley and Tom Robinson. Even Scout sees the comparison at the end of the book, when it is decided not to reveal to the town that Boo was responsible for Bob Ewell's death. He would have been the town hero, but that would have been like releasing the hounds to the fox--in a good but overwhelming way. He would not have been able to withstand all the attention. Tom is another innocent figure who did nothing more than an act of human kindness for a young, lonely girl. That "song" of kindness was cut short and he was sentenced and shot, despite his innocence. Like Atticus says, that's a sin.
The last quote comes at the end of Atticus's closing argument at Tom's trial. The entire speech is worth quoting, but I'm confident you already know the piece:
"Now, gentlemen, in this country our courts are the great levelers. In our courts, all men are created equal. I'm no idealist to believe firmly in the integrity of our courts and of our jury system. That's no ideal to me. That is a living, working reality!
Now I am confident that you gentlemen will review without passion the evidence that you have heard, come to a decision, and restore this man to his family.
In the name of God, do your duty. In the name of God, believe Tom Robinson."
There's more to the speech, of course, but this is a reflection of Atticus's belief in the law, in his fellow man, and in the innocence of his client. Atticus does not believe everyone is innocent, of course; he does, however, believe that innocent people should and can be treated fairly in the name of the law and in the name of God--and despite their skin color.
That should get you started, and don't be surprised if the list gets too long to deal with effectively!