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Your proficiency bonus doesn't go up every level. It starts at +2 and goes up by +1 at levels 5 and 9. You get to boost your stat (or take a feat) at levels 4, 8 and 12.
That's the short of it. You also can use spells in combat to increase your chance to hit, Bless being the obvious one at low levels.
Most attacks are tied to an attribute modifier. Melee weapon attacks use Strength by default (finesse weapons allow the user to use Dexterity if it's better), ranged weapon attacks use Dexterity, spell attacks use the spellcasting modifier associated with however the spell was granted (e.g. wizards use intelligence, clerics use wisdom, etc).
BG3 does not implement any rules regarding cover, but it does consider height difference -- a ranged attack from above gets a bonus, a ranged attack from below gets a penalty.
If, say, you take the Great Weapon Master or Sharpshooter feats on a character, be sure to deactivate the option that allows a -5 to hit / +10 to damage choice for when you don't think the trade-off is worth it. That -5 to hit can be really painful if your odds to hit weren't already rather good.
Advantage and disadvantage can matter a lot, because both mean rolling two twenty-sided dice with the former meaning that the higher is taken while the latter forces using the lower die. Attacking an enemy who can't see you is an example of something that grants advantage; making a ranged attack while an enemy is adjacent to you (regardless of whether it's the target of the ranged attack) grants disadvantage.
The level one Cleric spell "Bless" is notable for for granting its targets a bonus to hit.
Getting an advantage has a big effect because there's two rolls and the best is kept, and in case it's against you and you have the advantage, there's two rolls for enemy and the worst is kept.
And in case there's advantage or disadvantage on both sides, it's cancelled.
From this you need investigate what can give you advantage.
That doesn't really matter. I recently started playing and have already realized huge flaws with this game. For example, I used a fighter, with a +5 to hit mind you, and fought against 2 enemies with 13 and 12 AC. The percentage to roll numbers is so ♥♥♥♥♥♥ that all I got was a 2, 3, 3, 5, and a 7. They need to fix the RNG for rolling in this game, because it seems like it's nothing but percentage based. Like, it feels as if you have a higher chance to roll below 10 than you do to roll above 10. Thanks for reading, and BG3. . . Fix the game buds.
darkvision or lights on the enemy if they are in a dark area.
elevation, esp for ranged attacks
advantage, from various effects (knock-down (prone) is a key one)
magic weapons (+3 means 15% better chance to hit, 5% per bonus point on a d20)
various effects and spells like bless
high primary stat (eg if you hit someone with a 2h sword you need str to be high, if you attack with a wizard spell you need int to be high, ..)
armor reduction (eg make them stand in acid)
more attacks so if you miss one you still do some damage. There are many ways to get 3 attacks pretty early in the game (around level 5). A stock cleric with 1 shot per turn vs a multi-classed one with 2 or 3 is a huge difference in the first half of the game, but you have to decide how much magic to give up (for me, a str cleric with 1 level of monk gets me by for much of the game, but you can give up more to get more).
But also relatively intuitive is surround an enemy, at least when you use multiple melee, and remind that it's only the second hitting that get advantage.
Attack from stealth should also give advantage if I remember well, but here it's more about exploit stealth damages anyway. Still in some cases it can help remind it to increase a chance to hit.
Doesn't mean anything, though.