Check your skill trees often
In the game, each character has skill trees, which progress when you gain SP from various sources such as reaching landmarks or winning battles. You may find that you want to switch skill trees to earn a skill in a different tree instead of continuing to progress down the one you have set. Also, there will come a point where you've finished the tree and sitting on it won't be of value unless you want the specific passive bonus inherent to it. All in all, checking your skill trees often is a good way to maximise the efficiency of progress, as well as allow you to keep optimising your skill links between your party members.
Quick Step is a godsend of a skill
It allows you to run around the overworld faster, something you come to appreciate when you realise how colossal the areas are.
Try to pick up as many quests as possible before selling off items and entering them into collectopaedia
Collectopaedia bonuses and money are nice, but for the types who like doing all the side quests, nothing is more annoying than needing to get another rare spawn because you used it for something else. There is a mechanic which lets you know that items are needed for something, but it doesn't proc on everything (at least in the original) Speaking of which...
Check named NPCs for their trade offers
Named NPCs can offer trades, and this may save you some time with regards to getting quest items. It may also get you some other nice stuff. Take note that more trades can open up as you increase an area's affinity as well.
Use different times to survey places at different times of day
Quest and monster spawns can vary by time of day, so be mindful of that in the early going. It's something you'll have noticed eventually, but it's nice to be mindful of it sooner rather than later.
It's never too late to experiment with the character that just entered your party
Xenoblade Chronicles is a really long game, and as such when you end up getting accumulating party members, you may feel you've invested a lot of time and thought into your current party, and might not have the time to play catch up learning others. Trust me, there's plenty of time.
I've avoided tips on battle mechanics because the fun of the game is discovering the system for yourself. Besides, if you want to look that aspect up, I'm sure plenty of discussion exists for it already.