Isle of Songs
Fi says that you are on the Isle of Songs, certainly created by the Goddess for the chosen one. Read the stele which says to rotate the pedestal right next to it, and also take a look at the mechanism on the left withholding three crystals: a green one on the left, a blue one above and a blue one to the right, and call Fi to learn more about it. Notice the three circles on the ground where is, on each of them, a small block indicating the position of the corresponding part of the island. Also notice the huge blocks on some of the circles that block one moment or another the smaller blocks in their way.
By hitting the crystals and rotating the pedestal, you will understand that the inner circle is in fact the closest part of the island (inside), the middle circle is the second moving island (middle) and the outer circle is in fact the farthest part of the island (outside).
When the left crystal gets hit (it will turn green), the outer part of the island can move without getting blocked, when the top crystal is hit (it will turn green), the middle part of the island can move freely without getting blocked and when the right crystal is hit (it will turn green), the inner and outer parts of the island can move freely.
This is about how it works. Your objective is to succeed in aligning the three parts of the islands and to put them in front of the tower to create a bridge.
To succeed, there are several solutions. Here is Yanou38's solution and its logic:
Let's say that A, B, C are the parts of the bridge, A being the farthest one (outside), start by pushing the pedestal to align A with B. This is the first goal: A and B are aligned and must stay so until the end. Now you have to align C with A+B. Keep on hitting the crystals so C gets stuck and A+B finally end up with C, but A+B must never get separated, so you have to hit a crystal each time A or B gets blocked. But you should not wait for A or B to get blocked to hit a crystal. After a few hits, A, B and C are aligned. You now have to hit the crystals so A+B+C move together until they reach the north tower. To make it shorter, it goes like this: Stand behind the pedestal and push it 8 times to align A with B, then hit the top crystal and push the pedestal twice. Hit the right crystal, push the pedestal twice, then hit again the top crystal and push the pedestal 10 times. Hit the left crystal and push the pedestal 9 times. A, B and C are now aligned. Now you just have to hit the right crystal to unlock the three parts and push the pedestal 4 times until it's in front of the tower.
Here is another easier (and faster) way, but without any apparent logic: Without hitting the crystals, stand behind the pedestal and make it rotate until you align the outer part of the island with the inner one (to 9 hour). Then hit the right crystal and push the pedestal until all three parts of the island are aligned, then hit the top crystal and push the pedestal until the outer part of the island gets stuck (to 11 hour). Finally hit the left crystal and push the pedestal once to create the bridge towards the tower.
Cross this newly created bridge and get in the small passage. Stand on the circle, aim at the Goddess' crest and perform a Skyward Strike. A huge statue of the Goddess will appear and Fi hears the words the statue is whispering:
He who seeks the sacred flames, listen well, for I guide you from my place at the edge of time.
The sacred flames are three in number. To obtain them, you must also earn relics known as the three sacred gifts.
For each trial you overcome, you shall be blessed with one of the gifts...
Make use of the power of these gifts, and you will find your way to the purifying sacred flames.
Now, I bestow unto you a melody. It will serve you as a key, opening the first trial that awaits you deep in the wilds of Faron Woods.
Once she has performed a wonderful dance on this exquisite melody, Fi will add that this brave melody that will lead you is called "Farore's Courage", so you just learnt Farore's Courage! For each sacred flame, you will have to get through a trial to obtain a sacred relic and you can now dowse the gate of the first trial.
Leave this tower and this island, get back to Skyloft and dowse to confirm that the trial takes place in Faron Woods. Fly towards the green beam of light and choose the "Viewing Platform" as a landing point.
Head southwest, towards a place without grass and with a cloud of butterflies. Play your Harp and Fi will appear and sing along with your music. The "Farore's Courage" made a rosette (the Trial Gate) appear on the ground. Following her advice, get in the circle and thrust your sword into the ground! You are now in one of the Silent Realms, a spiritual world that can be entered only by the Goddess's chosen hero, the "Farore's Silent Realm". As your soul temporarily left your body, you receive the Spirit Vessel, a flower representing your soul's maturity. To fill it, you have to collect 15 Tears of Farore scattered around the Realm, while avoiding to be hit by the "guardians".
FYI: The order to pick up the tears isn't important, but here is what seems to me to be the fastest way:
Go straight ahead to pick up the first tear, then go ahead to find a Light Fruit that will show the location of the remaining tears for 30 seconds. Climb the stairs to the Viewing platform to get the second tear, along with another fruit, then get on the ledge of the balcony and jump down to the right. Dash straight ahead to pick up the third tear, then once between two "upright roots", climb on the one to the right, get on the vines, go left, jump towards the second vines, let go a bit further and pick up the fourth tear. Jump down and Fi will tell you about a liquid called "waking water" that you must not touch. Get on the log to cross this liquid and pick up the fifth tear along with a Dusk Relic further to your right, then cross the log back. Go on south (on your left) to find the sixth tear. Get in the small passage, pick up another fruit, then rush up the slope more or less in front of you while avoiding to be detected by the ghosts. Go left, then go across on the rope and pick up the seventh tear.
Pick up the Light Fruit as well, then get back on the rope and go on straight ahead towards the eighth tear. Pick up another Dusk Relic, then get back to the crossroad of this upper part and jump lower to the right to get the ninth tear, along with a fruit to the right. Go down and to the right (west of the map) towards some sort of light gate and pick up the tenth tear. Then turn around, go right, pick up a fruit and you will get the eleventh tear at the end of the path (to the far south according to the map). Backtrack again and go more or less straight ahead, a little bit to the right while going up several "floors" and pick up the twelfth and thirteenth tears which are close to each other. Go on to the right (east of the map), jump down (you will slide on a slope), then dash it up, pick up another fruit along with the fourteenth tear a little further. Go on right (north of the map), go up two "floors", go left and pick up the fifteenth tear! You just have to push the log in front of you, then jump and run to the circle where the trial started.
Check the forest map with the 15 tears
As a reward, you will receive the Water Dragon's Scale! one of the Goddess's relics, which will allow you to swim and to spin underwater. Fi congratulates you and says that the flame is somewhere within the forest, probably in a place you haven't visited yet. Speak with the Elder who will also congratulate you, then go south of the Great Tree, get into the water, dive and get into the tunnel. Swim through the bubbles to refill your air and get out on the other side.
Inside the great tree
Swim towards the vines, climb them, then turn towards the moving platform and jump on it. Use the Gust Bellows to get rid of the Froaks and also to make the platform swing. Jump to the next one, hit the Bokoblin, jump ahead and get out. Outside, climb left, then look upwards. Use the Slingshot to clear out the Walltulas, then grab the vines, move to the left, then let go when you're almost out of stamina. Get rid of more Walltulas, then keep on going towards left using the vines and get into the tree trunk.
A Moblin is here! Go slightly ahead, then throw a bomb at it to destroy its shield! Then rush to it and strike it as much as you can before it fights back. Hit it again several times, then get out and go on climbing towards the summit of the tree. Fight off the Bokoblins and the Keeses, climb the vines, and you will reach the top of the tree.
Fi shows you a snoring Kikwi. Launch your Beetle at him to wake him up. He introduces himself as the Kikwi Hermit Yerbal, watching over the forest when he's not napping ^^. Ask him where the flame is and swear to keep it a secret. The Kikwi informs you that it's called "Farore's Flame" and that it has been entrusted to the great spirit protecting the Faron Woods: the Water Dragon. He adds that this dragon lives in the huge lake south of the forest, but that the door leading there is closed. To open it, you have to infuse the seal carved on this door with the power of the Goddess, but a part of the carving is gone and to complete it, you have to find a symbol identical to the one on the door. After advising you to be polite with the grumpy Miss Water Dragon, jump down the tree and head towards the viewing platform. Get to the place leading into the woods and take a look at the drawing on the ground. Having engraved this drawing into your memory thanks to Fi's advice, go south of the forest, in front of the door you previously noticed. Call Fi, perform a Skyward Strike, then draw a circle inside the small crescent with the tip of your sword. The door opens! Get in the corridor and dive!