After the talk with Gaepora you can claim another 5 ruppees from the wardrobe. Head outside to finally see Fi. Follow her to the statue of the Goddess. You'll have to do some acrobatics to do that, but eventually you'll reach a hidden entrance behind the statue.
Fi will finally introduce herself (itself?) to you, after which you get to finally pull out the Goddess Sword. The next few minutes are heavy with talk and explanation. At the end of it all you'll receive the Emerald Tablet.
Functions: Skyward Strike, Dowsing, Fi-Captioning
Next stage: Goddess Longsword
How to obtain: Once you wake up after Zelda gets sucked down to the surface, follow Fi past a series of obstacles and into the Goddess Statue to access the Skyloft Shrine. At the heart of the shrine, withdraw the sword from its pedestal and it's all yours.
Description: This is the sword left in Skyloft by Her Grace, the goddess. It has sacred powers the hero can use against evil. Its guardian spirit, Fi, is the hero's servant and guide.
As Fi instructed, stand in front of the crest, charge your sword and shoot off a beam to activate it. Examine the altar to place the tablet and open the path to the first surface area. After all is said and done, there are some preparations to be made before heading out.
First off, as you leave Gaepora's office, you'll receive the Adventure Pouch, a critical item in the game.
Functions: Holds your secondary items (shields, potions, etc.)
Upgrades: Adventure Pouch Expansion
How to obtain: Given to you by Fledge after receiving the Hero's Tunic.
Description: The Adventure Pouch holds all kinds of backup supplies for ambitious adventurers. For you, this means shields, bottles, and occasionally some other stuff as well... You'll receive it as a gift before you take your first trip down to the surface world. It can only hold a certain number of items at a time, so be sure to make good use of the Item Check in the Skyloft Bazaar to swap out items as you need them.
First point of order is going to the sparring hall and talking to the Knight Captain. He'll instruct you to get a shield, and you'll be able to get a few things along the way as well. Head to the Bazaar in the middle of Skyloft. There are loads of shops here, you're interested in the one ran by the skinny guy on speed. Buy a shield for 50 ruppees and head to the other side, the potion shop. You'll receive a bottle and can buy a red potion for 20 ruppees.
Weaknesses: Fire, melee attacks, magic
Upgrades: Banded Shield
How to obtain: You can purchase a Wooden Shield at the Skyloft Bazaar for 50 Rupees.
Description: This is a basic Skyloft knight's shield. It's made of wood, so it burns and breaks easily. Upgrade it at the Scrap Shop to improve its durability.
I am still unsure however how a shield can fit into a pouch. Oh well...
Now you can go back to the sparring hall and receive shield training. Once you're done you're all set to go. Jump off from Skyloft and call your bird. Look for a green column of light and fly to it. You'll be prompted to dive through the opening once you are on top.