Stack buffs. As long as it has a different icon, it stacks. For attack you can stack attack up(twice for 1.5x total), madness (2x), phalanx(1.5x), resins(1.05x each), self mutilation(broken sword skill,1.5x). Probably another one or two I am forgetting.
Critical hits do 3x damage.
Using good attacks and taking advantage of damage vulnerability. Not all attacks have the same total damage. Like demonbeast hunter's saw's bloodedge has really high total damage and it inherents element (which not all skills can do but most do) so it does bonus damage if the enemy is weak to an element you are using (which is all of them besides light if you are using resins). But Kishingatana's iai strike has relatively low damage, doing about 15% as much damage but has no cooldown. Some of the strongest attacks are han's normal attack (at +5), zex sturm (+10 spear), moon bardiche (+10 halberd, also relies on magic so weak if you are using -100% magic gear), deadman's blow (+10 broken sword, also needs low hp ~10%). For magic, heavy soul discharge and soul stream are your hardest hitters. Catherine wheels too but you might not have that yet.
Break makes enemies take double damage (triple for hard break) from non guaranteed hit skills. If the enemy isn't immune, oil jars can make them weak to fire while frozen magic bullets can make them weak to ice and if you can inflict bleed on them, butcher's axe gives you 2x damage.
Of course, just having high stats helps as well. Using black souls boosts all your stats permanently.
I'm not sure if it's allowed to write the word lol