There is a short, slightly biased summary and a longer, more informative case synopsis. The largest collection of information about the case seems to be at http://www.wm3.org.
In a nutshell, the police investigation fed on a rumor mill and suspicion created by the police. When Damien was first questioned, he repeated the local rumors about the murders to the police, and the police believed that the only source of this information had to be from someone with first hand knowledge of the murders. With this belief, the police then concentrated on Damien and Jason, ignoring other possible suspects. When a young boy, prompted by his mother, confessed to the police that he witnessed the murders, his bizarre, unsubstantiated story didn't stop police from asking him to identify Damien and Jason in a line up (he failed). Because his story changed several times and other witnesses could place him away from the crime scene at the time of the murders, his testimony was never used, but word spread of a witness. (The boy's mother would later claim that she attended a Satanic meeting with Damien and Jason, and after the trial recanted the story.) Another person, William Winfred Jones, told police that he heard Damien confess to killing the boys, but recanted before the trial.
The young boy's baby sitter, Jessie MissKelley, was questioned by police a month after the murders, without a written waiver of his Miranda rights by his father (Jessie was 17 at the time, a minor). After being questioned (including 3 hours that were not recorded), Jessie confessed that he, Jason, and Damien committed the murders, although he needed to be prompted by police to correctly identify the mutilated boy, and that he had several notable errors in his confession, including, but not limited to, the time of the murders, how the victims were bound, the time of the murders, how the boys were tortured, and where the murders took place. (Due to the lack of blood, it is unlikely that the boys were killed where they were found.)
With Damien's occult interest and Jessie's confession, the police arrested the boys and searched their homes, seizing some items. The police would later claim that fibers from the crime scene were similar to fibers from the trio's homes, including a match to Jason's mother's red robe, and a match to the green shirt of a child relative to Damien. Defense disputed this in court, claiming that the fibers found at the crime scene could match any number of common household items. In addition, a serrated knife was found in a lake behind Jason's home, but could not be linked to Jason. A necklace that Damien was wearing at the time (and that was also worn by Jason) had two drops of blood - the first was the same as Damien's blood type, the second was the same as Jason's and one of the victims. There was not enough blood present for DNA samples. Due to legal reasons, the state never presented this evidence at the trial.
The emphasis on Damien might have seemed more justifiable if there were no other plausible suspects. Yet in a bizarre twist, on the night of the murders, a black man covered in blood and mud was seen at a local fast food restaurant, and spent an hour in the bath room, cleaning himself. Although police were called, nobody went into the restaurant to investigate. Blood samples later taken from the bathroom were lost. There was a negroid hair found on one of the corpses, but none of the boys or the accused were black.
One of the boy's stepfather also had some bits of circumstantial evidence pointing towards him - a knife of his had some blood which was the same type as him and his son's, and a hair at the crime scene was similar to his hair (the hair was also similar to Damien's hair). Non-therapeutic amounts of a drug that the stepfather and the boy used were in the boy's bloodstream at the time of the boy's death - the drug, Carbamazepine, depresses the central nervous system and can cause drowsiness in large doses. The stepfather was on friendly terms with the cops and was a drug informant at the time - fueling speculation that the cops might have overlooked evidence pointing towards him as a suspect. (The stepchild had signs of healed past physical abuse.)
Obviously the above are limited highlights of the case, and I encourage all of you to read the links and decide for yourself. My impression of the case is that it shows serious flaws, and that the trial is bizarre, especially the focus on the occult and Satanism. Perhaps the boys are not innocent of the crime, but I do not see how, in an unbiased courtroom with proper legal defense, they could have been found guilty beyond a reasonable doubt. Thus, I consider the case of the West Memphis Three a perfect example of the flaws in the justice system.