The best place to look for any recent metagame changes is the Smogon Metagames subforum. It has different subforums for every mainstream meta, and every recent change can be viewed in the same.
The viability rankings for different tiers are usually kept up-to-date, mainly because they offer a rough overview of a metagame. Every major update is followed by a "reasonings" post which concisely explains every raise or drop of different Pokémons. Most of these posts also attach the voting slate where the council had voted for the changes in the rankings.
SQSA threads (Simple Question, Simple Answer) threads are also a great place to ask small questions and begin with a metagame. For active metagames, you'll find fresh questions tackling the most recent changes/edits in the metagame. Active players would soon post an answer for most minor questions.
Team bazaars are updated with the most recent teams to showcase the metagame. You'll find teams of varying viability; make sure to check a team's viability and how it works before using it.
Good cores threads contain the best cores in the metagame. Cores are typically made up of two or more Pokémon that, when incorporated into the same team, work excellently toward engineering a definite goal. They're also a worthwhile place to linger around before starting to build your teams.
Outside the threads, the usage stats are good for checking the latest metagame trends and what most players laddering would use, in different rankings. (Thanks sumwun for this point.) These aren't very appropriate for lesser played OMs and other tiers because their ladders are horrible, though.
The Smogon Formats Dex is not a beneficial place to start learning about a meta. They take a lot of time to get vetted and approved before being uploaded, and consequently, a lot of analyses aren't up-to-date. This is especially common for the lower tiers and Other Metagames, which do not have as many active contributors as compared to the main formats.
There are a lot of different resources and threads which can help you cope with metagame shifts and changes. Lurking in the forums and Showdown! competitive rooms are the best way to get a better grasp of any metagame.
