Rules of evidence are governed by the branch of law and criminal justice called Criminal Procedure. A couple of concepts and rules are the exclusionary rule and the fruit of the poisonous tree doctrine. The exclusionary rule states in part that any evidence obtained by law enforcement agencies that was illegally obtained will be excluded at trial. Search and seizure doctrine is a good example of this. For example, say a police officer obtained some evidence without first procuring a search warrant, assuming of course that a warrant was necessary, that evidence irregardless of what it is, will be excluded at trial. Police officers want to do a good job and catch the bad guy so to speak, but the rules of criminal procedure must be followed to prevent over-reaching by the government. Not to mention situations in which the evidence in question may have been planted near the defendant in an effort to bolster the case and convict the alleged perpetrator.
Building off the first answer, the idea of procedural hearings to help determine the worth as well as the prejudicial value of admitted evidence can go very far in providing a fair trial. Lawyers have the right to question not only the evidence presented, but whether or not the presentation of said evidence would taint procedural due process and unduly influence a jury in one way or another. The ability for both sides to critique the presentation of evidence helps to ensure that a sense of fairness is present in the process of administering justice. It also helps to drive home the idea that fairness and respect for the integrity of the proceedings is at the forefront of both the counselors' mind as well as the judge who presides over the hearing. The ability to include or exclude evidence and hold hearings on whether or not specific evidence can be presented helps to bring the ideal of a fair trial into focus.
This is a pretty broad question, but I will try to give an answer that can illuminate one part of it at least.
I would say that a fair trial comes out of the prohibition on evidence that cannot be personally validated by a witness. As an example of this, think about the general prohibition on hearsay evidence. If I am accused of robbery, the prosecutor cannot call someone to testify that they heard that I committed a robbery. The prosecutor would have to call the person who actually said I committed the robbery. This gives me (through my lawyer, most likely) the chance to challenge the witness.
This requirement that all evidence be subject to interrogation in the court helps ensure a fair trial.