The whole point of a good prologue is to do something that the writer cannot do in the main part of the story without violating some important aspect of storytelling, like chronology or viewpoint or continuity. For instance, if the main story is told entirely from the viewpoint of one central character and takes place over the course of six days, except for one critical scene that takes place twenty years before the POV character was even born, that one scene is a clear candidate for being made into a prologue. Similarly, if there’s a ton of background detail and information that the reader truly needs in order to get through Chapter One, but which would bog that chapter down to a snail’s pace, a cultural/historical summary prologue may be in order.
One needs to be very, very cautious about deciding that you really need a prologue to do whatever-it-is. There are very few things that a writer truly cannot do without resorting to a prologue. Adding a prologue may be the first and most obvious thing the author thinks of when faced with a recalcitrant bit of backstory or characterization, but that doesn’t always make a prologue the best choice. Easy and obvious are not the same as effective.
On the other hand, while it may be quite possible to have your archeologists discover letters or a diary discussing life in Pompeii, it really isn’t plausible for them to find a first-person account written by somebody as they were fleeing the erupting volcano. The archeologists can piece things together and imagine what it must have been like, but if the author needs that dramatic flight scene as a scene, he’s probably going to have to put it in a prologue.
The second thing to remember about prologues is that if a book has a prologue, the prologue is the start of the book. The prologue doesn’t have to be full of action, any more than any other opening of a story does, but it does have to pique the reader’s interest so that they’ll keep reading. (This is why so many “ancient myth” and “historical background” prologues fail – they’re just not very interesting on their own.)
The third thing to remember is that no matter how brilliant your prologue is, there are going to be readers who skip it on principle. This means that a book with a prologue has, in essence, two different places (the prologue and Chapter 1) that each have to function as the start of the story (i.e., hook the reader into reading more).
Depending on the sort of prologue you’re doing, this usually means that Chapter 1 is going to have to start even more strongly than it normally would, in order to re-hook the readers when they have to switch gears, however slightly, at the end of the prologue. (Note that I said “start strong,” not “start with action.” There’s a difference.)
Prologues come in several varieties, and it helps to have some idea which sort you are doing. The different kinds of prologues tend to fall into categories according to timing, viewpoint, and style/function.
Timing: a prologue can happen before/long before the action of the main story; at the same time as the main story; or look backward after the main story is over. Viewpoint: The prologue can be told from the point of view of the main character from the main story, from the point of view of a secondary character, or from the point of view of some other character who never actually appears in the main story as a character (as with Steven Brust’s Paarfi novels, where the POV of the prologue is a crabby Dragaeran historian who is the putative author of the “historical fiction” that follows). Style/function: The prologue can be a scene; it can be narrative in a style different from but related to the main story (as when the prologue is a fairy tale or myth, or a summary of the historical background, or a fictional academic introduction to the material that follows); it can function as an introduction to the world or characters, or as a frame (usually with an epilog in the same vein) for the main story.
All of these aspects can be mixed and matched to some extent; that is, your prologue may be a dramatized scene from your protagonist’s childhood or a first-person protagonist’s narrative introduction to his memoir (setting the prologue solidly in the “future” of the main story); it can be a myth from your world’s ancient history or a centuries-in-the-story’s-future mythologized version of the events in the story; and so on.
A good prologue should leave the reader with more questions than simply “How does this tie in to the main story?” or “What happens to these people next?” This is especially important if the prologue is from a different viewpoint than the main story, because if the only thing the reader wants to know is what happens to these people next, she’s likely to get annoyed when the main story turns out to be about somebody else.
Generally speaking, a good prologue requires the reader to switch gears (from one time period to another, one viewpoint to another, one style/structure/format to another, or all of the above) between the prologue and Chapter One. The bigger the shift in gears, the stronger your opening of Ch. 1 has to be to re-catch and re-interest the reader. If there is no shift of gears between the end of the prologue and the beginning of Chapter 1, then what you have is probably actually Chapter 1 and not a prologue after all, and all you really need to do is renumber your chapters.
In addition to all of the above stuff, prologues are usually significantly shorter than the average chapter in the rest of the book. This isn’t an actual format requirement, but it is well to remember that the more one can condense the scene or information, the more likely one is to get at least some of those readers who hate prologues to read it anyway. On the other hand, three pages of super-neutronium-density narrative summary are likely to put off more readers than one might lose with a ten-page scene that conveys less actual information but keeps the reader interested with less effort on their part. It really depends on what you’re trying to do.