Atticus is not connected to Tom outside of the fact that he is appointed by the court to represent Tom in court. Calpurnia, Atticus' maid and surrogate mother for Jem and Scout, attends the same church the Robinsons attend. Atticus will know more about Tom Robinson and his integrity through Calpurnia.
Atticus loves all people and wants to see the guilty punished and the innocent go free. He truly believes Tom is innocent and pushes to prove this fact in court. He does prove it--everyone is aware that the Ewells are lying--but because Tom is black and his accusers are white, he is convicted.
Atticus Finch is Tom Robinson's court-appointed defender for Tom's rape trial. Tom, as a black man in 1930s Alabama, has already been convicted in the court of public opinion, but Atticus still takes the case seriously and does his best to exonerate Tom, who is innocent. Atticus knows that because of the entrenched racial prejudice in Maycomb that he will not win the case, but decides that the right thing to do is to fight for Tom anyway.