Please take a look at these guides I wrote for an introduction to the Riot API and using/understanding JSON.
While you can use many languages like PHP, I teach it in Javascript/Ajax/JQuery as that knowledge than be applied to other languages pretty easily, especially with PHP since the syntax of both look decently similar.
[Tutorial] Beginners introduction to Riot API and JSON, using Javascript and Ajax
I discuss what the API is and how you use it, as well as securing your key. I also mention JSON and how to access and understand it with a program.
Let me know if you have any questions.
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solved Riot Api – Json