Getting Yang to rejoin your party and the Sylph Summon
The Sylph summon is technically the secondary reward for completing this side quest since the actual reward is Yang joining your party again. You begin this side quest when you're in the Underworld by speaking to Yang who is asleep in the Sylvan Cave. If you've forgotten where the Sylvan Cave is check out Chapter 9 <Add Link> of my walkthrough.
Once you've spoken to Yang you'll want to talk to his Wife who is located in Fabul. If you've forgotten where she is, she's found in the western tower on the third floor. She'll give you the Frying Pan item which you'll want to use on Yang who is asleep in the Sylvan Cave. Doing this will get Yang to rejoin you and reward you with the Sylph summon.
For another reward return to Yang's wife and give her the Frying Pan she gave you. You'll receive the Spoon in return which you can use as a Throw on Edge to hit an enemy for 9000+ damage. Pretty useful for any of the upcoming tough boss fights!