Writing in hand gestures and non-verbal communication is kind of tricky. They are deeply cultural symbols, interpreted by a specific group of people. To outsiders, they seem like nonsense. But non-verbal communication is a form of communication, which may be included in a story. Sometimes, a character, for some reason, does not verbally say anything, but makes a hand gesture instead. How do authors deal with these culturally-bound gestures?
Unless you know that a particular gesture is going to be well understood by your readers it is often better to write it from the perspective of a third party, either character or narrator. Essentially present it in terms of what that character understands by it ie focus on the perceived meaning rather than describing the gesture itself.
Obviously some basic gestures like a shrug or nod have well established nouns.
For example you could say
John gave a half-shrug which failed to convey much enthusiasm for the idea.
The driver indicated his displeasure with a simple but emphatic hand gesture.
Dave indicated with a surprisingly eloquent gesture exactly what he though Steve could do with his article.
Albert gave his reluctant assent with a curt nod.
A weary shake of his head was his only response.
All of these get the meaning across without getting bogged down in visual descriptions.
If something is really culturally specific and important to the story you might want to go into more detail but you don't want to do it too often unless you have a really good reason.
The thing I miss in each of these answers is that hand gesturing and non-verbal communication should be treated like any other language.
There are always 2 parties. One is sending the signals, in this case not words but gesturing and other kind of non-verbal communication. and the other is receiving.
Clearly the non-verbal gesturing made by someone mean something but how the opposite side responds to this is up to interpretation and leaves you open for a variety of responses.
The key to making gestures or non-verbal communication work is describing how the opposite side responds to these gestures. As well as describing what the one sending the non-verbal communication means with his movements.
This way it is unimportant what is culture,because now you as author are in control of what movements are made and how it is interpreted.
The nicest way I've ever seen of pointing out hand gestures and body language in a narrative without disrupting it was to not specify what the hand gestures/body language are/is but simply to note that it exists. "X signaled the group and they [whatever]" as an example, or may favourite one when pointing out expressive hand gestures "if you tied X's hands they'd be struck dumb", "the way X stood clearly said [a thing]". These are efficient and within the context of the narrative quite subtle nods to that fact that humans communicate at least as much without speaking as we do by making noises.
Some gestures are universally understood. For example:
The audience burst in applause.
Because those gestures are universally understood, giving them description or explanation is redundant: you wouldn't say "he moved his head up and down, signifying assent".
On the other side of the spectrum, there are gestures that are culture-specific, and not likely to be understood by your audience. (Or they might be unique to some fantasy culture.) To use @DoubleU's example,
With her index finger, she gently scraped the side of her cheek - a subtle way of saying 'ugly'.
Because your readers are unlikely to understand what the gesture means, you need to explain.
If a particular gesture is going to be used more than once throughout the narration, you can describe it once, give it a name, and use the name from then on:
Kneeling upright and with her back straight in formal mipa rari, she composed herself [...]Kuni leaned back on his pillow and stretched out his legs in a modified thakrido position, with one leg over the other, the way a man sat when he was with his mistress. (Ken Liu, The Grace of Kings, chapter 3)
(It doesn't particularly matter if mipa rari and thakrido are names of existing poses in a real culture, or a fantasy terms for something in a fantasy culture. What matters is that from then on, the author can use the terms as often as he likes, conveying both an image and a meaning.)
Alternatively, a gesture might be common, but have different meanings depending on context. @MatthewDave's example of a cutting motion is an example of such a gesture. Here too you'd need to say what is meant by the gesture, unless your context makes it very clear. Or, you could have fun with it, having characters misunderstand each other's non-verbal communication:
As methods of human communication go, a wink is quite versatile. You can say a lot with a wink, For example, the new nun's wink said:
Where the hell have you been? Baby B has been born, we're ready to make the switch, and here's you in the wrong room with the Adversary, Destroyer of Kings, Angel of the Bottomless Pit, Great Beast that is called Dragon, Prince of This World, Father of Lies, Spawn of Satan, and Lord of Darkness, drinking tea. Do you realise I've nearly been shot?
And as far as she was concerned, Sister Mary's answering wink meant: Here's the Adversary, Destroyer of Kings, Angel of the Bottomless Pit, Great Beast that is called Dragon, Prince of This World, Father of Lies, Spawn of Satan and Lord of Darkness, and I can't talk now because there's this outsider here.
Whereas Sister Mary, on the other hand, had thought that the orderly's wink was more on the lines of:
Well done, Sister Mary - switched over the babies all by herself. Now indicate to me the superfluous child and I shall remove it and let you get on with your tea with his Royal Excellency the American Culture.
And therefore her own wink had meant:
There you go, dearie; that's Baby B, now take him away and leave me to chat to his Excellency. I've always wanted to ask him why they have those tall buildings with all the mirrors on them.
(Terry Pratchett and Neil Gaiman, Good Omens)
The most complicated are the gestures that are likely to be understood when seen, especially in context, but don't have a one-word description like "nod" or "shrug". Writing is a textual medium, not a visual one. As such, it is stronger in conveying some things, and weaker at others, compared to film, for example. With those, I think you have several options.
You can skip the particulars of the gesture entirely, and go straight to its meaning:
He made an obscene hand gesture
It doesn't particularly matter which hand gesture.
Or you could actually describe the particular movement. The trouble with that approach is that it takes longer than the actual movement, it is cumbersome. You would do it, I think, only when you want to linger on a particular moment.
I laid my hand on my heart, held it there for a moment, and then moved it over and touched my palm against his breast. (Juliet Marillier, Daughter of the Forest, chapter 15)
See also the question Describing body language? for more information.
He stuck out a middle finger.
This is a form of non-verbal communication in America. It is highly vulgar and offensive. I remember reading somewhere that this gesture is associated with the resemblance to the human penis and the word "Fuck You". Fuck is an obscene term, but when used literally, it can mean "having sexual intercourse with". Sticking out the middle finger looks like a human penis, and this "human penis" combined with the verbal "fuck off" means "go away" in a very offensive way.
With an index finger, she gently scraped the side of her cheek.
This is also a form of non-verbal communication. The gesture (forefingers rub) means "shame," and is restricted to North America. But scraping against the cheek with (typically) the index finger is a sign of shame or ugliness in Chinese culture. If someone displays nakedness or reveals too much skin, then the immodest dress would be seen as 丑. That means "not good looking" or the opposite of "good looking" and "beautiful". The finger is rubbed against the face, because the face is a concept in Chinese culture.
Most people probably take the symbols of their environment for granted. When I first learned of the Chinese number gestures as a child, I didn't interpret them as Chinese gestures for numbers. I interpreted them as numeric hand gestures. When I saw my mother scraping her finger against her cheek, I interpreted it as "not good looking". I learned later, much later, that North Americans had a different hand gesture for a similar concept - the rubbing of fingers together. But I never actually witnessed this in real life, just read about the gesture online.
TLDR: I think an author may try to give a footnote at the bottom, referring to the back of the book for reference and cultural notes. Then, at the back of the book, the author may write a description about the face and other Chinese cultural concepts, so non-Chinese readers can understand it.
Make the gestures culture-neutral, or describe the intent of the hand gesture. For example:
He gestured across his neck with a cutting motion.
This generally implies decapitation, meaning anything from 'you're dead' to 'call off the action', but either way, given a context, the communication is clear regardless of culture. Loss of one's head is sort of a universal concern for humanity.
Well! It's easy if you are using Third Person narrative. You can explain about a gesture everytime a character uses it(first few times of course) . But if it's first person narrative, you need to make the scene very clear to the reader so that they'll understand what the character means by a particular gesture. And It's better if you create your own gestures for your work.