Sound design my dude! The basics of it is combining sound from a bunch of sources (library, custom recordings, synths) that fit the thematic of the character you're trying to build, and processing the sounds in the computer to create one single sound. Then combining a bunch of sounds together in game to create the sound of one ability. The average ability will have sound for the cast, the sound of it traveling through the air, the sound of it hitting a minion, a different sound for hitting a champion, and sometimes more, depending on the ability. Then each of those sounds will have multiple variations, so each time you do the ability it sounds a little different.
There are currently about 9 of us that do all the sound design for everything in LoL. Every sound in game is a custom asset made by someone on the team. And there's sound for pretty much everything whether you notice it or not (even mushrooms in the jungle have sound).
We have a library of stuff (explosions, animals, guns, different materials, hits, foley etc. + a bunch of custom assets we've created for champs and skins) that we dip into, but we also go out and record different things as often as we can, depending on what project we are currently working on. For example, we recorded a bunch of vegetables breaking for the Zombie Nunu and Slayer skins, or RiotKatateMoney recorded a bunch of rocks smashing and falling for the poppy rework. We also do smaller recordings for smaller things in game - Snowday Bard's meep-guins are sound designers making penguin sounds, Arcade Riven's "K.O.!!!" is the voice of the sound designer that did all her SFX, the harmonica in High Noon Jhin's ult was myself playing it in my room, then processed a bunch, all of Rek Sai's VO was various animals combined with different sound designers vocals; there's a ton of different examples.
Not sure if that really answered your question, but that's the short version of what we do. Were you looking for something a little more specific on how we make a sound?