After you receive the Goddess Sword and activate the Emerald Tablet, you can descend to the surface.
Land in the Sealed Grounds
Press the indicated button while falling to use your Sailcloth to land without injury. After a cutscene, go along the path and you will encounter Deku Babas. You have to swing your sword in the direction that its mouth is open. Otherwise, the attack won't hurt it. Just try a vertical and horizontal slash and see how it affects each type. You'll soon learn which attacks work on which types.
Continue going along the path, defeat more Deku Babas, then jump down to the ground below. After a cutscene, your next task is to go to the bottom of the big pit. You can run down to the bottom of the pit if you want to, but there is nothing interesting along the way. Just jump down and use the Sailcloth to safely get to the bottom.
At the Bottom of the Pit
You will be asked to use a Skyward Strike on the stone in the center. Get close enough to target it, then point the sword up and hold it still to charge it up, then swing the sword in the direction of the stone. Doing so will activate a bunch of air spouts around the area.
Fi will tell you how to use your sword for dowsing. When choosing your target, choose Zelda. Then move the sword around. You will hear a sound when you are pointing in the right direction. As you get closer, the purple ring in the center of the screen will have an arrow on it. Point toward the arrow until the purple ring is just glowing and there is a rapid dowsing sound. This means that you are pointing straight at the item that you are dowsing for.
Use this to move in the correct direction to reach Zelda. Use the air spouts to float up to the higher levels of the pit. Just walk onto an air spout and you will automatically float up on the Sailcloth.
Go Toward Zelda
The dowsing signal leads back to the sealed door up above. That door will unlock when you approach it, so go through. Save the game at the nearby statue, then go to the east side of the stairs, where you find a treasure chest. There is a Revitalizing Potion inside. This gives you an additional bottle.
Then go to the west side of the stairs and break the jars to find a fairy. If you bought a potion earlier, you should use it now even if you don't need it, and then use the empty bottle near the fairy to scoop it up. The fairy will revive you if you die. After a fairy revives you, it will disappear, so be sure to look for another fairy if that happens. To avoid accidentally using the fairy, you may wish to unequip and re-equip your shield. Hold the Pouch button to do so. That way, the pouch button will be set to the shield instead of the bottled fairy.
Now go upstairs. After you listen to what the Old One has to say, you can put a beacon on your map at the red X. Before you leave, you can look through the crack in the door behind the Old One to see something interesting. Then you can exit through the door that is unlocked for you.
Rescue the Goron
Go through the door that the Old One unlocked. If you aren't sure which one it is, check the map. It's the east door. Or you can dowse and go in the direction of Zelda.
Outside, you find some Bokoblins surrounding a Goron. Go up and attack the Bokoblins. You might need to bash them with your shield in order to get them to drop their defenses. (Press the Help button if you aren't sure how to do a Shield Bash.) Swing your sword in the direction that they are not blocking with their swords.
After you defeat the Bokoblins, Gorko the Goron will talk to you about Bird Statues. In addition to saving the game, you can use Bird Statues on the Surface to return to the sky. Then from Skyloft, just fly into to the column of green light again to return to the Surface. The first time you do this, Fi will tell you that she can send you back to any Bird Statue that you found on the surface, so be sure to check on each Bird Statue that you find. If you want to, you can return to Skyloft now to repair your shield if you need to (Gondo at the Bazaar can repair it), or buy more equipment.
Back on the surface, look around the area where you saved the Goron to see a cave entrance on a ledge. Climb up the ivy and go into the cave, then walk up to the log and press the indicated buttons to push the log off the edge. This gives you a shortcut to the Sealed Grounds.
Go to Faron Woods
Head toward the beacon that you placed on your map with the Old One's help. In the Nintendo Switch version, Fi will tell you that you can now use amiibo. If you have the Zelda and Loftwing amiibo, you can use it to instantly move between the sky and the surface. Using it on the surface will send you to the sky, and using it in a location in the sky will send you to the last place that you used it on the surface (if you haven't used it on the surface, you won't be able to use it from the sky until the next time you use it on the surface). You can't use it at night (i.e. after sleeping in a bed in Skyloft or another location in the sky) and there are certain locations and situations where it can't be used.
Continue going toward the beacon. Roll the log over to the wall, then dash up. From there, you can continue on to Faron Woods.