This is quite simple; you just have to tap on your desired character and then on "Stats". On the left bar, you will spot a button named "Upgrades". This will show all the upgrades you are able to do with this specific character.
What we want here are the mini upgrades that contain Weapon Skills. They are in all weapon forms: spear, bow, shotgun, and bomb. They will also have a green plus (+) sign near them.
Once you reach those on your progression, you will have the ability to purchase them. Sometimes they appear on the mandatory mini upgrades, and sometimes they are on the extra ones. You can decide what's the best course of action based on your gameplay strategy! :)
Now that you know how to collect them, it's easy! Tap on "Weapons" and select which aspect of the weapon you want to improve: knockback, velocity, range, cooldown, and/or radius. This will vary with the type of weapon. Remember, the way that each character uses their weapon is different, so this also affects which skills you can improve. You can select between the three different weapons in the right upper corner.
Each skill point will increase a percentage of the standard stats for each weapon according to the desired aspect you changed. Again, what you decide here depends all on the way you like to play. You can test different strategies and redistribute the points as much as you want!
And that's all for Skill Points! We hope you have fun, and if you wanna read more about upgrades, tap here.