Enhancing the intelligibility of a recording is like restoring the painting of an old master. With a combination of judgment and skill, the expert must remove interfering sounds, which are the acoustic equivalents of dust and grime on a painting, without distorting the original. However, the acoustic expert has a big advantage in that he can work with a copy rather than the original.
The best way to make a copy of a recording for enhancemant is to digitize the original recording directly into a computer. That is to say, to process the original recording through equipment that turns the recording into a series of numbers in a computer. If this is done properly, it causes no harm to the original recording. Then the expert can work with the numbers in the computer that represent the sounds. Whenever a copy is made, it is important to make copies through electrical connections between recorders or between the recorder and the computer rather than by putting the microphone of one recorder next to the speaker of another, which will introduce excessive distortion.
The tools most often used by in acoustic restoration are acoustic filters, which are devices or computer programs that let some sounds pass through unimpeded, while causing others to stay behind. You can think of them as being like coffee filters that allow the liquid coffee to pass, while keeping the unwanted grounds behind. Similarly, an acoustic filter can allow speech sounds to pass through while holding back noise.
I usually prepare an exhibit of the enhanced recording, in which the words or other sounds of interest are separated from the rest of the recording. This exhibit can be played to the trier of fact so they can hear the evidence for themselves.
An interesting case of enhancement was the Rodney King case, in which I suppressed the noise of a helicopter hovering overhead so that the voices of the arresting officers could be heard. I was the final witness for King, and played a section of the enhanced recording for the jury.