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Details vary, but there are usually some common ideas.
People have different initial growth rates or specializations, often called spiritual roots, or physiques, or aptitudes. Like, someone's good with fire, someone's strong, etc.
There are various cultivation (meditation) techniques, with different pros and cons. They can be good or bad, specialised or general, etc. They might be based on a mantra to be repeated, or on visualisation, actually moving through a kata-like form, and so on. Often, the cultivation methods come with some attacks, but attackscan also be learned separately. Cultivation methods are sometimes limited to a specific stage and have to be replaced once the person grows strong enough, but sometimes it thoroughly determines one's path and destiny and you just follow along.
Cultivation takes energy of the world (qi), and does something with it. Some areas are rich in qi and make it easy to cultivate; usually these are untouched and lush mountains. Others are spiritually empty, and cultivation requires resources, like stones of solidified spirit stuff.
There are specific stages, which seem to be based on how real Taoists thought they could reach immortality. First stage purifies the body and makes the body stronger, then at some point some supernatural powers become available. It's often associated with the body's meridians, which are Chinese traditional medicine's take on nerves or something similar.
At some point, a core or golden core is formed. It's usually seen as a mark of a rather powerful person. It's a ball of energy at a point below the navel called dantian. All sorts of supernatural things are possible.
Nascent Soul is one step further. The core turns into a spiritual child, which starts to grow into a spiritual avatar of the person. Again, I understand this is based on old Taoist beliefs.
Often, there are a few more stages between the ones mentioned above. Stages after nascent soul vary a lot between stories. Immortals, gods, devas, paragons, etc.
Some stories do something different, of course, but that's the most common thing.
If compared to a game system, each stage is like a D&D class or prestige class, chosen by following a specific cultivation method. Each stage has 9 or 10 levels or so, after which you get a new prestige class and a significant powerup. And perhaps a lightning bolt to the face, because heavens don't like mortals becoming immortals - it depends on the story.
To advance, you need both understanding (experience points) and qi (energy). Meditation gathers energy and gives understanding. Fights can also help with understanding (exp points), and various items like potions, elixirs and magic stones can give more energy, but some meditation is still required. This is a very banal explanation, and lacks all the fluff and details that make it interesting.
The translations available in English are varied and all over the internet. There are sites or blogs where a single translator or translator group posts, and there are bigger sites that show translations by multiple independent translators.
I first got into the stories through the site called Wuxiaworld. Wuxia in the name actually is a different genre, more of a low fantasy or martial arts type of story, but most of the stories there are high fantasy.
They host Child of Light, which I mentioned before. They also have I Shall Seal The Heavens, a series I particularly liked. It's very long though - there's no need to read all of it to understand the basics of the system.
I remember the story Desolate Era having a nice feeling to its system. It's also on wuxiaworld.
In it, understanding of easier concepts opens the way for more difficult paths (daos). The protagonist studies the sword, starts to incorporate aspects of rain into it, which turns into understanding of the concept of rainwater, and later, raindrop. Raindrop them would be a part of water, of the five elements. The understanding of the sword could also move towards the great and rare Destruction. The series is super long and the system was only explained slowly, though, so it might not be the best to get the understanding of the basics.
In general, I'd suggest giving a try to several different stories. They tend to have catchy starts, and the premise of the system is usually explained early on. Many stories have either a strong and wise mentor figure explaining things, or even have the protagonist be an all-knowing figure starting from 0 again (Emperor's Domination, Tales of Demons & Gods, Sovereign of the Three somethings).
There's a Chinese web novel company called Qidian international that hosts many novels on their site webnovel.com . There are some ongoing legal arguments with them and other groups regarding rights to the Chinese novels, their English translations, and who can or can not host what at whichever site.
One notable story there is Throne of the Magical Arcana. It is a take on a Western mefieval fantasy world in the process of magic-science revolution. It's a mix of D&D and the cultivation system more typical to Chinese novels. It has peer-reviewed magical studies published in arcana journals, and draws parallels between scientific theories and magic. Like, schools of astrology and necromancy, next to a newly discovered schools of electromagnetism. The story itself isn't great, but some of the ideas are very good.
Throne of Magical Arcana has a person make a connection with a specific star. This also happens in another story, Ze Tian Ji or Way of Changes. It's something like finding your own astrological sign that influences your fate. Ze Tian Ji is more thoughtful story than most others, and isn't as much of a pure wish fulfillment. The protagonist there ends up teaching various people very specific cultivation methods that specifically fit them, but I don't remember the specifics. It's only available on a different site, called Gravity Tales.