Whether imposed for a seemingly random reason or the greater good, nerfs to our favorite champions suck. It’s terrible to have power stripped away from you. However, there are ways to recover.
See what pros are up to. You won’t be able to see their reaction from tournament matches, since league servers are usually a bit behind on patches. However, pros play SoloQ and stream live, so nerfs hit them at the same time as you. This is where you become all ears (and eyes): watch open stream VODs or match histories to see how the best competitors are adjusting.
A good example is Kalista. Riot Games kept nerfing her to target the pro scene, but pros just started picking safer supports with her. It took the devs lowering the numbers into oblivion for teams to drop the pick.
Try altering your item builds and runes. Nerfs to a champion may be shipped with buffs to items that the champion usually buys. You may often see this with ADCs whenever the devs are trying to weaken S+ champions and keep the variety in itemization.
The net positive changes may appear disconnected. For example, Lucian has been repeatedly nerfed as an ADC-caster, but has since changed to penetration/Lethality with the help of new items.
If nothing works, take a break from the champion. It’s always useful to expand your pool, even if this isn’t something you wanted to do. Extra characters up your sleeve will make you less prone to future nerfs and make your play style a harder target for the balance team sharpshooters.
Seriously, if nothing seems to work after a patch, take a deep breath and slow down. As unpleasant as it is, the severity of nerfs or your current level of play may make you hit an unbreakable wall. Excessive attempts to push through it will most likely cause frustration from the champion, the devs who nerfed the champion, and eventually the game. I hate to see people burn out from these attempts—so please, move on to a different pick if there’s no other option.