A story I am writing has the main character teleported to a fictional world where no one knows their language. How do I write having them learn the language of said world naturally? It is a constructed language and is extremely different from English.
Language acquisition in the real world has five phases, usually applied in the realm of child development, so your character's language learning process may be similar. This is especially true since your constructed language is very different from English, so English grammar, syntax and rules won't apply to help give your character a baseline - it will be essentially almost a blank slate. Their first language will not be as much help as it normally would. For example, if they natively spoke Spanish and were trying to learn French or English, their pre-existing grasp of how their own language is constructed and their grammar would help immensely, since those languages are very similar. But here, with a completely new conlang? Out the window!
(Here's a great source for all of this on the phases if you want to learn more.)
Stage 1: Pre-Production.
In this stage, also known as the "silent phase," your character cannot even speak any words in the language yet, let alone understand it. The languge and its phonemes, sounds and speech production are totally alien - it would be like if you were surrounded by Martian speech, literature and music and had no concept of how to process it or where to begin.
In order to advance past this stage, the character needs to make a concrete, dedicated effort to get started. You can't learn a completely new language by just absorbing it passively, even though immersion can help a lot - they'll need to work at it. They need to pay close attention to how other characters speak the language, trying to pick out individual words, sounds and an alphabet (if there is one). Are there particular sounds in your language that are more common than others, like greetings or goodbyes? Your character may notice these and try to figure out what they mean through context. They may ask other characters what the words and sounds mean, or find some other way to communicate, like charades or pictographs, until they're able to start grasping words.
Stage 2: Early Production.
In this stage, the character has grasped some basic words and sentences. They still struggle to comprehend the language, and must still pay close attention to native speakers to learn more words and common sentence structures, but they're now able to start experimenting on their own. Like a young toddler, they are able to construct very simple one and two-word sentences - "how are you", "go there," "hello", and so on. However, their speech is usually full of errors, like grammar and syntax errors. Think of a young child first learning the word "go" and how commonly they will make the error of assuming the past tense is "goed", and so on. This is where your character will trip up on common exceptions in your language - i.e. unusual words or exceptions to the usual grammar rules. The only way around those is to memorize them and move on.
Stage 3: Speech Emergence.
At this phase, your character has good comprehension. They can usually follow a native speaker when they speak, as long as the native speaker talks slowly and clearly, although faster native talkers may be completely lost on them. They can produce simple sentences that are more complex, such as "where can I find [item]?" and "how is your father?" They may still make grammar and pronunciation errors, but their overall grasp is stronger than before.
However, this is often the phase where jokes, idioms and metaphors are lost on them, since those represent unusual categories of speech. Your character might hear another character use an idiom and be baffled about what it means.
"We'll open that sthueirjeer of hsungi'efhiwh when we get to it," said Zork.
Via only stared uncomprehendingly. She couldn't imagine why you would ever fill a sthueirjeer with hsungi'efhiwh.
Stage 4: Intermediate Fluency.
Now your character is beginning to communicate and write in complex sentences, fully understand native speakers when they speak, and is overall confident in their language usage and control. They engage in academic learning more independently, can have discussions and conversations, and their brain doesn't have to work as hard to understand the language anymore - the understanding is now beginning to happen at the subconscious level rather than needing conscious work. This is the phase where people joke about "dreaming in French," since their brain is literally getting used to the language and incorporating it into their mind and thoughts. They have excellent comprehension overall and make few grammatical errors, and they have lost much of the stilted grammar that singled them out as a learner. However, occasionally it's still difficult for them to fully articulate more complex thoughts, and they would struggle to write an entire book in the language or convey a very long narrative.
Stage 5: Advanced Fluency.
This is the native phase and the final phase in language acquisition. Your character is now a native speaker - they tell jokes, they relate long stories, they have advanced and abstract discussions, and they sound almost indistinguishable from someone who has spoken that language their whole life. This is the point where an "accent" may emerge depending on their first language - have you ever heard the joke about how we all have accents, even if we can't hear them? Your character would probably still have an accent from their first native language while speaking the conlang, so it could be fun to imagine what that would sound like!
There are lots of other resources about how people acquire new languages, including in child development, so if this is something that interests you further, definitely look into it. I hope this helped.