How exactly does the sigil magic work? I think I've hopelessly confused myself.
Ok, so you learn one or more sigils and those give you access to specific spells. You need to learn at least one core sigil. Let's say I know the sigil of Earth - this gives me access to the Hold Portal spell. If later I learn the sigil of Focused Intent, I get access to the Stone Ram spell. Later, I learn the Fire sigil, giving me access to Produce Flame and Burning Hands (since I already know the Focused Intent sigil)...
So the sigils themselves do not have an effect, they unlock spells that you can use. Well, Enhancement sigils modify the spells, acting like metamagic in other systems.
I'll quote the text from the Sigil magic page to answer this:
"Characters can learn a number of magic sigils of any type equal to their PER. At first, learning a core sigil (first column) lets them cast a single spell (second column) even if they don’t know any expression sigil (first row) yet. As they progress, they can combine core and expression sigils to cast various spells, further modified by enhancement sigils."
Now, how they get their sigils is decided by the Referee. Are they found, do they research them... you decide.