Gearing is very similar to any mmo you've probably played where you can upgrade/level up the items. So for gear, right now, don't worry about upgrading much (aside from the requirements in your Adventure Book where it could say lvl up a weapon to 10). You'll get a 4* Sword at AR10 from the Adventure Guild rewards. Here is a vid showing how to enhance weapons:
Leveling up Character level is pretty much the same way. Select the character you want, and you should see an option to "Level Up" on the screen somewhere. That will open up a screen that shows you the various Books you've gotten, each type will give different amounts of XP, so try to use them smartly so you don't waste Xp by going over by a large amount.
Try to use the Adventure Book as a guide on what to do / try, since it wants you to do a lot, but it also gives pretty good rewards for doing them. If you don't have it by AR11, make sure to go talk to the Adventure Guild lady again (she is close to the entrance of Mondstadt). You have probably completed a lot of them already.
There is a chart on page 1 here showing how the various elements interact with each other, and making use of those interactions becomes more important as you go further into the game, especially vs. Shielded mages.
Now, I'm wondering if anyone here has come across this puzzle:
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Gotta find 4 of those little blue spirts and guide them to their resting spots, but I cannot find the 4th. This spot is West of Mondstadt in the area called "Wolvedom". I've ran all around this area, but that last spirit is mia.
Edit: Of course, just after I post this, I find the spirit behind a rock wall you need a Claymore user to break. Puzzle unlocks an AR16 Domain dungeon.