Before I answer this, I just want to make sure you know exactly what competitive battles (or the "metagame" as you call it) is. Simply put, basically any battle that take place between two (or more) people is a competitive battle, but they're almost always associated with the rules and tiers from a site called Smogon that I'm sure you've heard of.
"Competitive" battles are different from in-game as they require much more thought put into teambuilding and battles than an in-game battle against a computer does. A computer is just a program, but a person can plan ahead, predict and make intelligent moves that a computer could not achieve.
You might notice that I mention Smogon a lot in this. That's because they own basically the entire competitive Pokemon metagame. Their tiers are by far the most popular and balanced, but they are not in control of everything. Smogon doesn't control anything in-game and their rules are not official - you can play competitive games without the influence of their rules and tiers, but just keep in mind that most competitive games follow their rules. For example, the Pokemon VGC competitions are most definitely competitive battles, but they are official tournaments and aren't influenced by Smogon at all.
- "Can someone break down competitive battling to me?" - explains everything you should know before you play anything at all. I hit the character limit, so you might want to look up Smogon's rules and clauses yourself.
- Pokemon Showdown! - battle simulator, much better than in-game. Full support for Smogon tiers, and the battles function the same way they do in the game. If you're interested, this site PokemonDB has its own server on Showdown. Hopefully there'll be some members of the site there who'll be willing to practise with you :)
- PokeaimMD - fantastic competitive YouTuber. Watch his Showdown lives and such. He does good commentary and explains why he makes certain moves. He also has some useful guides on his channel.
- Guide to Pokemon roles - you'll see these sorts of thing mentioned a lot, so it's good to have an idea of what they are.
- Pokemon tier viability rankings - if you want to know which Pokemon are the most threatening, this might be useful. I try to keep it updated using my silent editing powers, but if it isn't up to date, follow the links to the Smogon thread that shows the most recent version.
- Practise, practise practise. Learn each Pokemon and what it does in the game, play games in the tiers you're interested in, get better at the game in general. Once you have that down, think about things like prediction and make game plans in team preview. What Pokemon do you need to win the game? How will you beat the opponent's team?
- Learn from others. Look at teams in the RMT section and learn from those. Also look at what people have to say about them - often people will point out errors in the team that you can also learn from. Watching shared replays of battles on Showdown might also help.
If you're new, remember that it's OK to lose. Even in the lower part of Showdown's ladder, most players are much more experienced than you are if you've never played competitive Pokemon before. As I said, just practise. It'll take some time, but you will get better.