title_body: How to "Naturalize" a Conlang?
upvoted_answer: There is one big point here that really ties it all together:
  
  Languages have history
  
  Any conlang that wishes to look naturalistic therefore needs to emulate history as well. I’ll show in what ways history can manifest with a bunch of examples from different areas.
  
  Orthography
  
  Almost no language with a history of writing has a fully regular orthography. Even if there are regular writing reforms, some aspects of the orthography will just be considered “part of it” and stick. English is of course a very extreme example of this, but you don’t need to take it that far. German for example generally has a rather regular orthography. But the digraph ⟨ie⟩ represents a long /iː/, reflecting that in the past (and in some dialects until the present) there was a diphthong /iə/ in German, which became to be pronounced that way. It also has two separate graphemes for the phonemes /ɛ eː/, namely ⟨e ä⟩, reflecting whether the sound originates from a fronted /a aː/ or not. On top of this, there are some segments which have unpredictable pronunciation: word final -ig for example is pronounced /ɪç/ instead of expected /ɪk/. In short, unless your writing system was designed very recently by linguists, it likely shows leftovers from the past. In the most extreme cases, writing systems can lag behind centuries (English, French, Tibetan), but even if they don’t they can preserve some old features.
  
  Morphology
  
  Most languages with inflections show some degree of irregularity among them. This can manifest in many degrees, from almost entirely regular (Swahili has only one class of six slightly irregular verbs, one of which is suppletive in the present tense) to a basically complete lack of predictability (Navajo verb stems have defied any attempts to find rules for their inflections thus far. There don’t seem to be distinct paradigms, every verb does its own thing!). However, these irregularities are not random. To show what I mean, compare these two sets of declensions. The first two are latin singular nouns (in an less traditional order), the second two made up on the spot.
  
  NOM filius rēx      kwero   tulya   
  VOC filiī  rēx      kwerap  tulte
  ACC filium rēgem    kweruf  tultsu
  GEN filiī  rēgis    kwerim  tulne
  DAT filiō  rēgī     kwerx   tulum
  ABL filiō  rēge     kwert   tulwo
  
  
  Two things should stick out: 
  
  
  The Latin forms of rēx show two distinct stems, those ending in /k/ (rēx, where the spelling hides the fact that really it’s rēc-s) and those ending in /g/ (all other forms). Looking a bit closer, we can see that the /g/ appears exactly before those forms with a vowel in the suffix. Intervocalic voicing (which accounts for /k/ becoming /g/) is a common sound change and applies here. 
  While in both languages, some of the affixes seem to be unrelated, there are still patterns: nominative takes -s, accusative takes -m, genitive has an -i in the suffix… If we added other paradigms into the comparison, even more such patterns would arise, indicating that they really originate from a much more regular system that got changed up over time by various factors like sound changes. In the made up language, on the other hand, the affixes are entirely random, and this causes the irregularity to look more unnatural than if everything took the same affixes.
  
  
  Phonology
  
  Consider the Japanese consonant inventory. It looks something like this (omitting allophones):
  
    m |   n |   ɴ |
  p b | t d | k g |
      | s z |     | h
      |   r |     |
      |   j |   w |
  
  
  What this table does not show however is that /p/ is significantly rarer than /t k/. Why would that be? Simply because many instances of that sound somewhat recently shifted to what is /h/ in modern Japanese. In other words, a sound change caused a significant imbalance in the distribution of sounds. If one were to simply generate words with a word generator, not paying attention to the history of the language, all sounds would show up with similar frequency. 
  
  Vocabulary
  
  If I give you any word, you can probably find several alternative ways of expressing that meaning. “big”, “tall”, “large”, “spacious”, “gigantic”… they all have different connotations, sure, but in the end they’re all descriptions for roughly the same thing - objects which take up a big fraction of your field of view when near them. Meanwhile, many conlangs will have a dictionary entry like gwop adj “big” and that’s it. Adding synonyms, especially ones with subtly different meanings allows you to greatly affect the way texts read (in a positive way). 
  
  At the same time however, often complicated words are derived from simpler concepts. This naturally has the effect of making them longer, causing a variation in the lengths of words - many short words with a few longer ones in-between is a common pattern. But if you simply create a new root every time you make a word, you won’t get that - and your hypothetical speakers will have to remember every single word without help, even ones they barely ever use. 
  
  
  
  I could go on and on and list things in every category of linguistics I can think of, but in the end it all boils down to this:
  
  Irregularity in languages either preserves older, then-regular systems in now untransparent ways (English verbs are another great case study for this) or are the creation of sound change messing with regularity. The former is the reason why common words tend to be less regular - if you commonly hear a word it’s easier to preserve its original form and remember the irregularity once it has arisen. In the case of Navajo I mentioned above, curiously it seems to be that first sound change caused irregularity, and then the native speakers applying analogy caused the whole system to become even more irregular. See the paper I linked above for some hypotheses on how that worked.
  
  Now, onto the actual question: Assume you have a conlang already, and it lacks history and is entirely too regular. “Sterile”, one might say. What can you do? I’d like to present you two options:
  
  
  Invent a history for your language. Sketch out how your verbal system may have looked in the past and see if you can lead that to some interesting irregular forms or alterations. Come up with some sound changes that may have led to the current state of the language. You don’t have to do this in great detail, but obviously (as always with conlangs) the more effort you put in, the better it will look.
  Make your language the history. If you don’t mind your end result potentially looking vastly different from what you have now, you can decide to move the  current state of the language into the past. You may have to make some changes to vocabulary to keep it in line with technology, but otherwise there’s not really any difference between a modern language and a “proto-language”. Then, you can track its changes through history in great detail, and in doing so introduce its natural flavour. No one has to know that the proto-language you worked from was unnaturalistic (but you’ll have to live with that knowledge. Just remember that you have to start somewhere, you can’t derive every conlang from the first utterances of mankind). 
  
  
  
  
  As a footnote, I’d like to make a book recommendation: The Unfolding of Language by Guy Deutscher. In this book, Deutscher discusses (in a very accessible manner) exactly what this question boils down to: how and why did languages become the way they are - messy and irregular and oh so complicated. I believe every conlanger should read this book, regardless of level of experience.