A mnemonic (/nəˈmɒnɪk/, the first “m” is silent) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory. Mnemonics make use of elaborative encoding, retrieval cues, and imagery as specific tools to encode any given information in a way that allows for efficient storage and retrieval. Mnemonics aid original information in becoming associated with something more accessible or meaningful—which, in turn, provides better retention of the information.
In the context of Chinese and Japanese characters mnemonics usually work by analysing the elements of a given graph in such a way that a short story can constructed. When the graph is a semantic compound, such an analysis may correspond to the original composition of the graph (for example “three trees 森 equal a forest”).
However, most graphs are phono-semantic; a number of frequent graphs are originally pictographic—but may be have become arbitrary signs through standardization; only very few are semantic compounds (and a lot of the semantic compounds have become unintelligible in their modern form as well).
In practice mnemonics are based on a reinterpretation of the (elements) of a graph and building a (highly subjective) memorable story.
The habit of reinterpreting graphs is almost as old as the graphs themselves are. A lot of the analyses of Xǔ Shèn (ca. 58–ca. 148 CE) amount to reinterpretations, because the origin of a lot of graphs was already lost at that time. People have been reinterpreting and telling stories about graphs ever since. Occasionally such stories turned out to be so compelling that they got firmly attached to a given graph. Mostly however, those stories are as subjective and as arbitrary as any mnemonic made up by a student.
Foreign students of the languages of China and Japan have to somehow catch up with the people in those countries and learn thousands of graphs that took those people decades to learn from an early age on. In the short term (especially if you have to do exams) mnemonics can help to remember all those different signs.
In the long term the usefulness of mnemonics diminishes. It seems that the best way to internalize the graphs is to engage with the language itself as much as possible. That is, reading and writing a lot. As you know more and more words well, instead of (separate) graphs you will learn to recognize those words and see past the graphs used to spell those words.
With writing things are a bit different than with reading. Reading and “passively” recognizing what is written on a page is different from writing and “actively” having to try to recall how to spell and write.
It used to be the case that repetition in writing graphs gave the student the “muscle memory” to thoughtlessly and fluently write them. However, most writing nowadays is done with input systems on computers, tablets and phones. (Some of those input systems might even use a voice interface.) As a result of depending on electronic devices, even native speakers seem to lose some of their ability so spell accurately.
Since it takes a lot of time and practice to get and retain the ability to write by hand, it might be more efficient to give up that ambition all together. You can stick to writing using electronic devices. On the other hand, if you have to do exams, or want to be able to make handwritten notes, or, if you feel honor bound to be able to write by hand, than mnemonics might still play some role (in addition to regular practice).
There are lots of books that claim to help with remembering Chinese and Japanese characters. Some of them give an (more or less reliable) graphical analysis of a character and offer perhaps one mnemonic. A recent example of that approach is The complete guide to Japanese Kanji: Remembering and understanding the 2,136 standard characters, by Christopher Seeley and Kenneth G. Henshall with Jiageng Fan.
On this website I also favour analyses that are historically credible, but I’d like to offer more mnemonics than one (if I can think of any memorable mnemonic at all that is; I also omit mnemonics for most pictograms).
Other books use methods that involve almost completely reinterpreting how characters are made up, in order to build a framework for building memorable mnemonics. The most famous example of that is the work by James Heisig. See the Wikipedia article Remembering the Kanji and Remembering the Hanzi.
To make mnemonics it is necessary to be able to analyse graphs into separate elements, and to be able to recall and name those element separately. How to memorably connect the parts is very subjective. According to the memory-training specialist Harry Lorayne, when trying to link items you have to make “the most ridiculous association that you could make”. This is different from the traditional method of making logical (and therefore somewhat boring) stories. See this short overview by Lorayne himself, or go and buy and read one of his (many) books.