Along the left side, you can only get the skills that come with your character. When you start out in the intro, it tells you "you were born with the soul of the endless" or something like that. Faintly along the outer left edge of the hexen scree is those names. You can only add the skills that match your god. You should most likely have at least one dot for yours, and you should be able to get the rest without any tasks. You cannot get any of the other skills on the left without special circumstances.
For the skills on the right, the ones that have concentric circles, you can only access those skills when you gain affinity with the related god. The top one is Gro-goroth, the second down is sylvian, and so on. The circles depict how much affinity with the god you need to get the skill. When you have affinity, there is a pale white light around the circles that are available; you can only get the skills within the white light.
I hope that answers your question!