I am trying to figure out the fastest way for skill Grinding. I just want to know, if I use a skill, will it increase the skill exp based on use? Or is it more so that I have to kill as many enemies as possible with one skill. I am not entirely sure which one is better or makes sense.

It's not that complex. Basically using the skill on any enemy will contribute to it. Level of the enemy doesn't matter and killing one or multiple targets with a single skill doesn't make a difference either. As far as I've observed.

My method for the fastest skill level grinding is I equip at least 3 cool down magatamas and run Kishinden Hell with an AFK party over and over while spamming only the skill I'm trying to level. Since any level mob will contribute I prefer Kishinden since there's a lot of enemies and they can be kill quickly. Also my combination of cool down magatamas leave me with only 252 hp so that is the only dungeon I really stand a chance at not getting one shotted by everything. Having Yoshitsune right outside is also convenient if you're trying to level a skill that uses a lot of durability.

Also it helps to raise momotaro's friendship level. I can't say how much of a difference it makes but one of his abilities that increase with friendship level is increasing skill leveling speed.

Well depending on your level, and if you can go to maru sewers, there's yoshitsune right there too and the mobs constantly respawn so it's easier to spam your skills there imo.
1. Cooldown magas help immensely.
2. Leveling Momo helps level skills faster.
3. Multiple weapons with the skill you're leveling helps you spam more. [unless you have 100 cd, then fk you t(-o-t)]

It's common sense but still. - 3 - I'm trying to help mate.