How do you stay current with the League of legends meta?

Meta is a term that applies in two worlds of League of Legends. Soloq/ranked environment as well as competitive play. We shall bear in mind, that strictly speaking these are two different games.
When it comes to meta for majority of the player base it wouldn't matter too much. If a player learns the fundamentals and stick to his own champion pool, within his own goal of getting better - most of the time it won't struck him of what is popular, or meta at the time. Of course, changes do happen and champions get changed. Map gets changed, items are different and the overall balance is rather at a satisfactory level, however CORE LEAGUE OF LEGENDS almost never change. Past these years, the core game is very much the same. Only and most recent change that involves game mechanics are the side lanes catching up faster with the center (mid) that changes dynamics a bit.
I myself play soloq from time to time and watch the KR & Chinese soloq streams as well as some VODs. Data is important too.

Mainly I watch and analyze LEC, LCS, and LCK games. I am also a fan of LS and YamatoCannon streams. They always provide useful information about current meta and champions tier lists.

Of course, besides watching PRO Leagues and streams of professional coaches, I check new patch notes on the official League of Legends website and I analyze by myself which champions or items could be strong in the newest patch. Finally, I share my knowledge with students.

Well... some people might disagree, but meta is indeed useless in 90% of the coaching cases unless a player aspires to become a pro. Talking about generic coaching; stats and best champions are non-existant, you can literally play everything, create your own build, as long as it's statistically not wrong, and you will go up by just your own will and some basic informations paired with some consistency. So yeah, we can pretty much say that the meta, is not something relevant especially when someone wants to learn, because often we misslead important informations, example: (meta items are the best items on a specific type of enviroment, but they are not statistically always the best ones!) So telling a player to buy x item because it's "meta" makes a lot of damage in the long run because after 3 months or so, they will not be able to play again because you didn't explain them basic concepts such as ad, armor crit scaling and so on..

There are multiple ways for me to keep up with the meta. Such as: Casting the competitve league, having multiple accounts for different roles and actively participating in tournaments.

As for my job being a caster for PCS , watching competitive scenes such as LCK and LPL constantly definitely helped me out a lot in terms of understanding the game at a bigger picture. For example, whenever a new tech or strat pops up from pros , I could then try to alter it a make them compatible for solo queue environment.

As for different roles and tournaments, they both provided me deep insights into how other players think in different circumstances (elo/roles/state of the game). It is benefitial for my coaching since I would then be able to kept on getting first-handed experience on all game changes.

I play soloqueue in every role and and almost every elo by playing on many different accounts. I test out theories when it comes to new patches and limit test a lot so I can give my students the latest news and trends on the league of legends meta.

Next to playing myself, I invest in research to find out the best 'ways for coaching people' so that I also stay up-to-date with the best ways to help my students understand new things.

Since I'm passionate about League of Legends I also follow most regions when it comes to pro play which also gives me a lot of info on the latest trends, ... .

I also participate in domestic proplay myself from time to time which helps me gain useful insights such as draft specific info, ... .

I am part of multiple Discord communities that focus on League: my server of friends, where you can pretty much always find someone playing league and anyone can jump in and watch a game live thanks to the share screen function, as well as my own coaching server where I keep track of all my past and currents students, post useful materials and hold my coaching session.

Apart from that, I read patch notes as soon as they come out (people usually post them on Twitter and a Discord bot notifies the entire server) so I can see what’s going to be new and impactful before it even hits the live servers.

I also watch a few community created guides and follow winrates/ tiers on sites like u.gg.

Playing the game in different elos is one of the best things you can do. Playing the game in, for example, Gold accounts for a couple hours will give you a way better grasp of the meta in those elos and allow you to coach them better.

So first of all coach and play in all elos. Metas are different in each elo.

Secondly, reading patch notes and following them closely.

Third, don't just follow what other pros are doing but rather understand why behind everything. Consume content as well.

Well it's pretty simple. Watching Youtube. Reading Patch notes and also playing league in all different ranks just to test the best picks that could be an OP tier pick for my any low-elo player. Every rank is on a different difficulty level and In my opinion every rank requires a particular champion that could easily 1v9 in that certain rank. and I love playing all champs. so It's not really a difficult thing for me to keep testing any OP/S Tier champion in whatever patch ^-^

I spend a lot of time playing in different ELOs in the ranked ladder. I play 1k+ games per season, as well as keep track of patch notes and strategies from both smurves on the ladder as well as higher ELO patterns. I also play in customs servers with other better players, to keep an ear to changes in the game in their experiences.