Every weapon type has 1 easy to obtain mod that increases its base damage, and these are CORE mods every weapon needs. These are:
Serration for rifles
Point Blank for shotguns
Hornet Strike for pistols
Pressure Point for melee
Just adding these won't be much of a difference as they only increase your damage by 15% by default. You actually need to rank these up in the "mods" menu by spending credits and ENDO (which is a resource you find in missions and get by cashing in dupes of other mods) and THEN they start adding much more damage to your weapons.
In addition to base damage mods, other core damage mods are all 4 elements (heat, cold, toxin, electricity) which straight up just add extra damage to weapons, and "multishot" mods which gives you a chance to fire 2 shots every time you pull the trigger, effectively doubling damage.
For more info on how to pull all these mods together to increase weapon damage check this video out. Invaluable stuff for a newbie that helped me greatly:
https://www.youtube.com/watch?v=1XKiWQHc1Ug