Just because a character is learning a language doesn’t mean you need to dump a bunch of information at the reader. By ‘information’ I mean the endless words that are not native to the language the story is in.
I think this is especially true for fantasy authors who may create their own.
Some authors are masters of creating languages, like J.R.R. Tolkien. We’re not all linguistic gurus, though, and we shouldn’t subject our readers to random strings of letters.
Not everyone loves Star Trek enough to learn Klingon, Vulcan, or any number of other created languages associated with it, and similarly most readers will not be pretending to be one of your creatures.
If you’re curious about creating a language, though, go here.
Don’t forget that characters might speak in programming languages or some other math-based jargon. That’s part of the beauty of creating a different world.
Just remember there’s no need to show off all the research you did. The story will be stronger most of the time without it.