Mechanically, the three things you're going to have to worry about are natures, EVs, and IVs that stray far away from what you're doing in game.
IVs: Individual values, they're going to determine semi-small differences in stats for your Pokemon, breeding is the main effective way (last time I checked) to get higher IVs in most games, chain SOS battles likely also have some mechanic that works with that in S/M & US/UM. Easy googles for IV guides exist, they aren't too hard to find.
EVs: Effort values, USUM and S/M made these super easy to train in-game this go around using SOS battles. I would once again recommend a quick google search along the lines of "EV Training in S/M." These values increase stats exponentially and are one of the largest impacts on a Pokemon's stats.
Natures: You've probably noticed each Pokemon has a nature, and the red/blue highlights on stats in later games make it a little more obvious. The nature of your Pokemon (with the exception of neutral natures) raises one stat by 10% and decreases another by 10%. Neutral natures like Hardy and Quirky just don't affect your stats in any way.
For making a team in your game, those things will get you started on understanding what mechanics competitive players are aware of and thinking about when they build their Pokemon. Of course, what moves your Pokemon has, the item it is holding, and the role it plays in your team get a little more complex.
Pokemon showdown is a simulator where you can use trial and error to simulate "perfect Pokemon" where you can just adjust these values online and get better at battling. I would highly recommend either googling teams, or finding a well-rated team off of the RMT that a reputable user has built and testing the water with those. Smogon specifically offers analysis on every Pokemon along with team suggestions and things to be wary of when using them.
My best suggestion would to be browse around teams from reputable sources (Depending on the user, our RMT, or Smogon boards where they've playtested teams) once you find a team with Pokemon you like, play test it on Pokemon showdown until you start getting comfortable. I'm sure there are still lots around here throughout the chat or DB server on showdown who could help talk you through things if you run into trouble.