In order to spend a skill point, you must find a Base Camp and rest there.
(The Siberian Wilderness walkthrough covers the mechanics in detail.) When this meter fills, you earn a Skill Point. Each time you gain XP, a shield-shaped meter appears on the left side of the screen showing the number of points earned.
As you progress through the game you'll gradually accrue Experience Points (XP) for things like hunting, defeating enemies, finding collectibles, and reaching new areas.