As
QXZ notes, flashbacks can play hell with narrative
coherence. If an
audience isn't aware that a scene or occurrence is intended to be a flashback and outside of the main narrative chronology, they may become confused ("Isn't he dead?") or misunderstand significant plot points ("I guess he's not dead, then."). As such, many artistic conventions have arisen to indicate a flashback, so that without disrupting the flow of the narrative, the audience might become aware of when the device is being used.
In books, the simplest way to indicate a flashback is to clearly indicate it as such. A chapter heading may include a notation of the time that it is set in, the beginning of the flashback may include descriptions of the setting or characters that is sufficiently different from how they were presented in the rest of the story to make it clear that the scene occurred in an earlier time, or the flashback may be preceded by pertinent text or dialogue (such as "I remember back in '38 when me and Jack took on the Hard Luck Brickyard Crew...") which serves to fix the setting in the reader's mind before the flashback itself is presented.
Brief flashbacks, if not otherwise indicated, are often presented in italics. Thoughts are often also presented in this way, too, however these are usually just one or a few sentences and, when treated in this manner, written as dialogue would be. Italicized flashbacks mostly last at least a full paragraph, and sometimes as long as a few pages (rarely more, however), and are written in the same style as the rest of the book, including action, descriptions of setting, and the like. Flashbacks are also often presented as personal reminiscences, and so a switch from third person to first person point of view may also signal a flashback.
As cinema and television are primarily visual media, artists in these media cannot directly communicate with their audience as easily as in the written form. Of course, they can just use writing, as is common in other instances where setting is not immediately clear, by subtitling the opening shots (often an establishing shot) of a scene with the time and/or place it is set ("Louisiana, 1875", or "November 22, 1963").
Beyond this, however, there are a variety of purely visual techniques at a filmmaker's disposal that operate by changing the "look" of a flashback scene. For example, the images may be made to look like they were recorded during the period the scene is set (black and white for the early 20th century, overly bright color for the late 50s or a slightly washed-out, grainy look for the '70s, etc.). Alternatively, by slightly blurring the picture, softening the focus, overexposing the film, or over-lighting a scene, the resultant pictures may take on a too-bright, slightly "unreal" feel that audiences will associate with the vagueness and slightly "off" quality of memory. This effect is also sometimes accomplished by heavily blurring or fading along the edges of the picture, or by adding a "sparkling" effect in postproduction. That other cinematic sense, sound, may also be manipulated for effect, as with the "selective hearing" of flashbacks in 12 Monkeys. Similar to these conventions is the use of blur or wavy dissolves during transitions to and from flashbacks, sometimes with a related musical bridge, as parodied in Wayne's World.
Employment of these techniques may be considered as dated, kitschy, or a sign of amateurism. In many cases, a good filmmaker can chronologically set a scene by paying close attention to details. A good deal of setting may be established through clothes, fashion, cars, hairstyles, the appearance of advertisements or other public displays, and reference to events or things peculiar to that era. Period music may also be employed to finish the atmospheric affect. While not a flashback, I would recommend Dazed and Confused as a splendid example of this attention to detail. Of course, this is of less use if the audience is not expected to be familiar with the era and location in which a flashback is set.
Animation mostly follows the traditions of film and television. It might be harder to implement some of the filters and effects, especially where they intend to call to mind the look of the medium in days past - a scene from The Simpsons using the colors (but nothing else) from The Jetsons would likely just confuse, while the use of black and white scenes is mostly played for humor value. However, due to its nature, animation is able to pull off some effects which would be unthinkable or less suited to other media. For example, in the anime series Revolutionary Girl Utena, characters in flashbacks are portrayed as faceless, featureless "mannequins" with smooth, black-hole black skin, while hair, clothes, and other inanimate objects remain fully colored and detailed.
I'm not familiar with conventions regarding flashbacks in theatre or oral storytelling, I could only imagine that the former might use peculiar lighting, artificial fog, or similar effects, while the latter would obviously be verbal in nature, involving tense shifts, framing devices, or perhaps changes in tone or use of voice.
Of course, this is all assuming that the author or director wants you to know that a scene is, in fact, a flashback. Some works actively seek to jar or confuse the audience by deviating from standard narrative practices. In such a case, these conventions will usually be ignored, as the audience is not supposed to be sure of a given scene's place in the chronology of the work.
If you can think of other conventions relating to flashbacks, please /msg me and I'll include them.