My top 5 tips would be:
#1: Save Often!
There are plenty of times when walking through a door or talking to someone will start an unforeseen battle. And don't be afraid to reset after losing a battle to save some money.
#2: Field Effects Are (Often) Not Your Friend!
The gym leader will always have an advantage over you. Definitely have at least 1 guy to set up your own terrain, destroy theirs, or create a weather effect.
#3: Explore the Map!
So many hidden nooks and crannies. And like Seal said, talk to the rocks. Rare, invisible items are plentiful and help keep your money up.
#4: Expand Your Team!
Having more than 6 guys really helps cover weaknesses you might not realize your team has. It nice before a gym battle to look at a squad of 10-12 trained and ready pokemon and pick which 6 you need. I'd also recommend keeping somebody with a killing move like perish song or destiny bond to make easy work of fighting the "boss" pokemon throughout the game.
#5: Do Your Research!
I always play with Bulbapedia or Serebii open. Really helpful to know exactly what your going up against or what moveset you're training towards. Oh, and don't forget the game is currently running off info from gen VII, ultra sun and moon.