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.