SP are earned only at the end of every encounter. The exact amount is up to the narrator, but there are general guidelines available based on the events that transpired. SP are not earned exclusively for killing monsters, but are meant as a reward for furthering the progress of the story (hence the name). While slaying evil creatures may be part of the plot, it is unlikely to be the only part; characters must engage with non-aggressive NPCs, seek clues to ferret out villains, and more.
Once SP are earned, they are added to any other SP the character has currently banked.
The character may then spend SP at any time outside of a dire situation on any unlocks or upgrades they see fit. To spend SP, simply reduce the total banked by the required amount, and then mark the unlock or upgrade on the appropriate location on the character sheet.
SP can be spent on any of the following:
NPCs do not earn SP; they cannot accrue them or spend them. Narrators may opt to grant NPCs upgrades over time to keep them in line with the PCs. Villains, in particular, may behave in this way; but in any event, this is not through the SP mechanic, which is for PCs only.