The invention of languages is the foundation. The 'stories' were made rather to provide a world for the languages than the reverse.

Gollum
© Inger Edelfeldt
How do people talk to one another in the imaginary world? What languages do they use? It is unlikely to be English!
Tolkien was a philologist, an expert in the history of languages and how they change over time. His job was also his passion - he invented new languages for fun. He spent much of his life making his inventions more complicated and realistic, especially the languages of the Elves: Quenya and Sindarin. He created Middle-earth as a place where the languages would be spoken.
The invention of new words for new things and ideas has become common in fantasy writing. These are usually just odd words or phrases, not entire new languages.

The Entrance to Moria
© Ted Nasmith
But these bits of invented speech don't often seem as real as Tolkien's. It takes more than just a handful of new words to create a believable new language. Quenya and Sindarin already existed before Lord of the Rings, and had far more than a few words and phrases.
As well as inventing new languages, you need a way of writing the words down. This can't be using our own alphabet. You need to make up a new way of writing, as Tolkien did with the Tengwar (like the top of this page). Or you could make changes to a real one, as he did with the Runes (like the bottom of this page).
This means thinking about how to write the sounds of the language. You could just swap a new letter for each of our alphabet letters. But watch out! The sounds of English can be quite slippery!
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Elen síla lúmenn' omentielvo
A star shines on the hour of our meeting