We have asked similar questions about languages and about flags, but what about the core of generational knowledge: Writing. Obviously symbols to complex or indistinguishable are bad, just as the symbols should match the writing system, but what about the lesser details?
What goes into making a good writing system?
I think first you have to define what you mean by good. There are three major types of writing systems that I know of, ideographic (Chinese, Egyptian hieroglyphs), alphabetic (English, Greek, Cyrillic), and syllabic (Japanese hiragana & katakana). Each has advantages & disadvantages.
Ideographic languages like Chinese have the advantage that they don't depend on sounds, so that people in different regions & time periods can still read documents even though their spoken languages has diverged to the point of mutual incomprehensibility. The disadvantage, of course, is the need to memorize a multitude of ideographs.
Purely alphabetic languages represent spoken sounds, which is both advantage and disadvantage. Advantage, because anything can be represented (e.g. phonetic alphabets). Disadvantages are that different regions may pronounce the same word differently, and many (all?) languages have homonyms, where one spoken work will have several meanings. English often gets around this problem with its 'irrational' spelling.
Syllabic writing is similar to alphabetic, but with more characters. I don't offhand know of any purely syllabic writing system (though Wikipedia lists a few). Japanese is a mixed system, with the main meaning of words carried by adaptions of Chinese characters (kanji), verb tenses &c in hiragana, and foreign loan words in katakana.
Chase the niche, not the average. Imagine some situation which has highly specialized demands upon it that are outside of the everyday, and you'll get something much more interesting. Here are some ideas do get your creativity flowing.
Most writing systems are based upon the documentation of a spoken language between people. But, what kind of writing system would you develop to record American sign language, or dance routines, or to systematically name plants, or describe astronomy observations? What if the purpose is to write down bird songs or insect chirps? What if the primary purpose of your writing system was to accurately describe human faces in a standardized way that was good enough to walk into a bar and pick out the right person from the description? These specialized writing systems could become universal in the way that the main system for writing down music has become today.
Eventually, those languages might even develop more general uses and become full fledged general purpose writing systems. The earliest writing systems from Serbia to Egypt to Pakistan weren't developed by poets or historians or priests or academics. They were developed by accountants, ration system bureaucrats and traveling merchants, mostly to keep track of connections between goods and people. Eventually, the accounting symbols were generalized for wider use.
What about a writing system designed for writing with your toes, or blinking your eyes at a computer, or having a computer user interface that tracked your eye movement, or with a stylus in your teeth, or that you would lick onto a surface, or claws, or that would utilize a prehensile tail?
What kind of writing system would be well suited to a sentient species that lived under water like dolphins or whales or mermaids?
What kind of writing system would people raised in China but never formally trained to read or write in any language develop?
What about a writing system that uses three-dimensional instead of two-dimensional characters? What about a writing system that maximizes information density by utilizing color, texture, thickness, orientation, and relative position context as well as character shape to convey meaning?
Why settle for one writing system for one language?
Japanese has four! (logographic kanji, which are adopted Chinese characters; the Latin script (rōmaji), syllabic hiragana, used primarily for native or naturalised Japanese words and grammatical elements, and syllabic katakana).
English has cursive (with upper and lower case), print (with upper and lower case), shorthand for certain specialist writers, and a small number of logograms (e.g. @ $ & #).
Urdu and Hindi are basically the same language, but in different scripts.
Some writing systems cross linguistic boundaries. Both Japanese and English share systems for writing music and mathematical and physical symbols, including recent writing system inventions like Feynman diagrams to summarize interactions in particle physics. Could a more efficient way to describe genetic code in writing be developed? What sort of writing system might an international system of notation for prostitutes develop? What about a notation system to describe personalities or to summarize interpersonal interactions in small to medium sized groups of people? What sort of writing system would surveyors in a place where nothing came in straight lines and nothing was on flat land develop to write legal descriptions in?
Writing systems always starts as symbolic graphs in some way called ideograms. As language and writing develops more ideograms are added either whole sale or combined from several other ideograms. These ideograms are detailed at first, but as people become more accustomed to them and need to use them they become simplified.
So to make a good writing system you have to start with a list of ideas that are commonly used. For example, the idea of "light" will come up often because when you describe the Sun and Moon you're going to say Light in the Sky during day/night or "Light off in the distance" or "small lights in the night sky" or "fire is hot light". "Light" becomes a very common base element and since many people will write it in many different contexts they'll start to simplify the basic shape.
Ideographic writing ends here, but we hardly ever see purely ideographic writing system. What we see is a combination of Ideographic symbols and symbols that have defined sounds and phonetic meanings. So a symbol, let's say "o", might mean "Light", but it will also have a sound associated with it like "oo" or "po" or anything else.
Eventually unused ideograms will stop being used or only used in specific cases. And this will be spurred on more by the phonetic writing system used because the phonetic system is easier and so more people will use it, simplify it more, and come up with rules of grammar and when to use ideograms, if at all (such as in Egyptian which uses both). This results in a general alphabet, chosen for its ease of use.
To note here, because people have different ideas of what is easy and which ideas are common to use you'll have several competing scripts which will eventually blend into each other or diverge as cultures diverge or blend.
What about what sounds go with which symbols. Simply speaking, it's not arbitrary but it is. Aliens likely have a different sense of these things, but humans connect sounds with texture, color, etc. This is called synesthesia. There are cases where the person has an extreme version of it, but all of us have it underlying a lot of the connections that we make randomly. So things that are "sharp" and "dangerous" are going to have a certain hardness and sharpness to it like "K" and "G" while others have a roundness and softness like "B" and "P" so at this point to get the "right" sound for the "right" symbol you simply need to rely on instinct and connect the sound with the idea that the symbol represents. If it's an alien tongue then that's pretty much out the window.
Once you got that... there's grammar, language evolution, etc. all of which is a lot more difficult to figure out if you're being more accurate and "good" at further developed written and non-written languages.
It depends whether you mean "good" as in "easy to learn and practical to use" or as in "believable as being the naturally evolved writing system of a fictional culture created by the author". The two meanings of a "good" writing system would give very different results. Most real life naturally evolved writing systems have irregularities, ambiguities, borrowings, complications and accretions of alleged shortcuts that were quite obviously cobbled together by some random scribe in a hurry and then just "stuck". Usually the longer the culture has used writing the worse these are.
The creation of a "good" writing system in the first, practical sense would be the work of years for scholars and scientifically trained experts. Among the systems in daily use by large numbers of people, the Korean Hangul alphabet is regarded as one of the most logical. An aspect of Hangul you could copy is that the shapes of the consonants iconically represent the shapes the human mouth makes when forming them. Then again, there are advantages to a purely arbitrary set of phonetic symbols such as the Latin letters I am using now: you do not have to fuss about getting the representation right, just ensure the symbols are distinct and quick to write. The symbol set should not be too large to learn easily. The full form of the International Phonetic Alphabet is incredibly useful to people who study languages in depth but would be too unwieldy for daily use.
An efficient writing system need not be phonetic at all. Systems of ideographic symbols have been created with the intention that they could be used as an auxiliary written language for people of different spoken languages, for example Blissymbols.
Turning to making a good writing system in the second sense, that is, one that is a believable outgrowth of a fictional culture, your starting point would be the physical form of the beings, human or otherwise, who used that form of writing, including what appendages, tools and materials they had to make permanent records. As ohwilleke's answer said, these could vary to an almost unimaginable degree.
Assuming human or human-like writers and an Earth-like world, your next step is to think about what materials they have to write with and on. For instance, runes that were originally cut into wood with a knife tend to be angular sets of straight lines. In contrast, forms of writing that were originally written on leaves tend to be based on circular shapes because cutting straight lines along the vein of the leaf would split it. The cuneiform writing of ancient Sumeria used a wedge shaped tool to press marks into soft clay. If your system's first scribes have something like parchment or paper, whether they use brushes or quills will make a difference to the style of writing that evolves.
Historically, logographic writing systems (such as Egyptian hieroglyphics or Chinese characters) preceded alphabets, syllabaries and similar sound-based systems. But they didn't long stay purely logographic, if they ever were. Quoting Wikipedia, "All logographic scripts ever used for natural languages rely on the rebus principle to extend a relatively limited set of logograms: A subset of characters is used for their phonetic values, either consonantal or syllabic." So if you intend to portray the writing of a society that has long been literate and has kept its traditional form of writing, a logographic system with an overlay of phonetic elements would be most plausible. Logographic systems tend to take longer to learn so writing is likely to be the preserve of an elite. This may be considered a feature not a bug.
Societies that are more recently literate, or where there has been a reform of the writing system, would probably use a phonographic system. The website "Omniglot" has a list of types here. Languages with a restricted set of syllables such as Japanese are likely to use a syllabary, languages such as Hebrew or Arabic where most of the meaning is carried in the consonants are likely to use an abjad, and so on. Because phonographic systems are usually easier to learn, a higher proportion of the people are likely to be literate where one is used.
Finally, when people are conquered or influenced by another religion or culture, this also is likely to affect their writing system. It is very difficult to force people to change their spoken language but replacing the writing system is much easier, especially if few people can read.
Creating a writing system is all about consistency.
Once you've got a base system designed, you build upon it based on the rules you've created and do not deviate.
I think that there are three main ways to go about making a new writing system - The first is to modify an existing one.
You can start with a basis like English, for example, and work off that. Create substitutes for letters, perhaps use the same rune for two or 3 uncommon letters to increase the differences between English and your system (stops it from being mapped 1:1 with English), or perhaps change a grammatical rule, like always writing all nouns before their descriptors. Things that were originally in English like "the large green apple dropped down" could be re-ordered to "the apple large green dropped down", as an example. As long as you follow the rules that you've set down the writing system will remain consistent for the most part.
The second possibility is to start from scratch - assume that the species you're creating this for doesn't speak. Create your runes to represent things, and figure out how you want to represent them. For example, you could base it off Chinese a bit and have different characters represent different elements/things, and then combine those to represent more complex things. Again, consistency is the key.
The final possibility is to start from a spoken language. For example, if you've already figured out how your species speaks and what sounds they can enunciate, simply create runes to represent all those sounds, you're good to go.
