Experience Points

Experience Points (XP) - you can gain them for discovery. This can be the discovery of something your character can use: an artifact. It can also just be the discovery of some new numenera procedure, device (something too big to be "equipment") or even knowledge. Lastly, depending on the outlook of the GM and the kind of campaign the group wants to play, it could be something as abstract as a truth. This could be an ethical idea such as "what goes around comes around", or it might be something like, "everyone has their price". Typically, discovery is going to earn PCs about half their experience points.

Using XP
Players decide how they want to use the xp they earn. There are short, medium, and long-term uses. The short-term, immediate use for an xp is that you can use 1 xp to immediately reroll any die on the table (even one someone else rolls). This is pretty straightforward.

Medium-term uses are a bit more costly (but not much) and are usually story-based. A player can spend xp, for example, while climbing through the mountains and say that these mountains are just like those found in the region where she grew up. In those mountains, she is skilled in climbing. This helps her at that time, and any time she might return, but it’s not as though she’s skilled in climb everywhere. This might cost about 2 xp. Alternatively, another character, with a bunch of numenera components, might spend xp to cobble together a device that allows him to breathe underwater, because he wants to explore a submerged complex. This gives him that ability for a considerable length of time but probably not permanently. Again, the story and the logic of what’s going on dictate the parameters.

Long-term uses of xp are more costly still, and permanently affect a character. For 4 xp, you can gain training in a skill, increase your stat pools, improve your ability to use effort, and so on. When you do this four times, you gain a level (which in and of itself has some advantages).