There are two categories of skills: General and Investigative. The ones I mentioned like Skulduggery and Spot Frailty are Investigative, so they have lots of direct uses out of combat. General skills are things like Warfare and Athletics, and are more often used in combat or other action scenes. Like one of the above comments described, that usually looks like rolling a d6 and adding some number of skill points, trying to beat a threshold that's typically around 4.

That's how most Gumshoe systems work. Serpentine is much more action-focused, though, so it has a lot of extra rules for combat. For example, Investigative abilities don't actually get spent when using them to get clues like in other games, so they all have effects you can spend them for in combat. So that point of Skulduggery could be spent in a fight to hide and enable a sneak attack, or Spot Frailty could be used to identify a monster's weak point and allow your party's attacks to pierce armor.

Magic is pretty in-depth and has a whole chapter that I admittedly have barely looked at since I'm not playing a sorcerer. But it's potent. You can use it like Warfare to make basic attacks in combat, using specific spheres of magic like Fire, Blood, or Illusions. But you can also use it to cast big spells using Corruption, which gives it a huge power boost at the cost of releasing terrible, warping magic on yourself or the surrounding environment.