Judge Taylor is the judge that oversees Tom Robinson's case. Atticus says that he is a good judge, which is saying a lot. He approached his position a bit casually but he always "kept a firm grip on any proceedings that came before him." He had an interesting habit of putting "a cigar into his mouth and munch[ing] it slowly up" only to spit it all out later on. He was "amiable, white-haired, slightly ruddy-faced". He often gave the impression of dozing but never did. During the case he maintains control, is a bit baffled by the Ewells, and seems to be fair and logical. I put a link below that will give you even more information on the judge, and a summary of the chapters that he appears in.
At the end of chapter 16, Judge Taylor is introduced and described. He is the judge in Atticus' case of Tom Robinson. Judge Taylor is described as "amiable, white-haired, slightly ruddy-faced, he was a man who ran his court with an alarming informality--he sometimes propped his feet up, he often cleaned his fingernails with his pocket knife."
In some of the longer hearings, Taylor sometimes appeared to be sleeping. However, he was never unaware of what was going on. One other interesting habit of his was that he didn't smoke cigars, but slowly chewed them down.
"If one was lucky, one had the privilege of watching him put a long dry cigar into his mouth and munch it slowly up. Bit by bit the dead cigar would disappear, to reappear some hours later as a flat slick mess, its essence extracted and mingling with Judge Taylor's digestive juices."
Later after the trial is over, the judge is spoken of again. He has a late night visitor one Sunday night. Maycomb knew it was Bob Ewell coming after him. Taylor made Bob look like a fool on the stand, and Bob was trying to get even, so Bob cut his screen that night.
Judge John Taylor is the man who appointed Atticus to take the Tom Robinson case. He is a very sensible and fair judge, who appoints Atticus as Robinson's defender because he knows that Atticus Finch can defend Robinson without bias. He is a very informal and sleepy sort of person, and he has faith in the justice system. He believes that the justice system will work, and he seems very fair in the courtroom, although he does have his own thoughts on the case. He seems a little out of it sometimes, but he really is paying attention, and he's the sort of judge that will snap to it and take care of things if things get out of hand.
Judge Taylor is a judge who judges Tom Robinson's case. He is a fair judge and believes in a proper trial. He is the one who appointed Atticus to take up the Tom Robinson case because he believed that Atticus would be the only one to properly take up Robinson's case with full proper fairness and care.
Judge Taylor is informal, relaxed, and fair. He is similar to Atticus, but he does not let his bias get in the way of the case, and he is determined to see the case through without giving a word either way. He has enough faith in the citizens of Maycomb that the jury will see the evidence and find him innocent. Whether that happens or not, you'll have to read. If you already read it, you know what happens.
(That book was actually based on a real case, and the woman who accused the man of rape was ashamed that she was left alone with him when a train broke down.)