To solve all the puzzles, use the following steps.

Before starting with the puzzles do following things:

Plant the seed that you find near the broken lift (see-saw like object). Just take a villager and drop it on the seed to plant it.
Light the fire at the fireplace in the village center. You can find wood near the left shore of the ocean and dry grass near the waterfalls (left of the amphitheatre).
Know the herbs. They are six of them. Five are present since the start of game and the sixth (the magic herb) appears once you reach the level 2 of Naturalist/Magician (noted in the tech). The herbs are as follows.

Lotus: Located near the Ancient Bath.
Black Orchid: Located next to the Roster Of The Dead.
Rose Plant: Located by the high fruit tree and the lift in the Orchard.
Tiger Lily: Located on the path to the door.
Cactus: Located to the right of the Research Lab.
Magic Herb: Either the Pitcher or the Berry Plant; located to the left of the Alchemy Lab.

The puzzles are in the following order:

Puzzle 1 Puzzle 2 Puzzle 3 Puzzle 4
Puzzle 5 Puzzle 6 Puzzle 7 Puzzle 8
Puzzle 9 Puzzle 10 Puzzle 11 Puzzle 12
Puzzle 13 Puzzle 14 Puzzle 15 Puzzle 16

Puzzle 1 - The First Tribal Chief: Let all your villagers one by one try on the golden cloth at the amphitheatre near the fallen statue. The robe will fit on the one that will be the first tribal chief.

Puzzle 2 - The Bee Hive: Before this puzzle, a fire should be lit in the village centre. Put one of your villagers at the burnt torches below the hive. It will pick up the torch and light it from the fireplace then take it to the hive to remove the bees. You can enjoy honey after this happens. However, honey is limited.

Puzzle 3 - The Alchemy Lab: This requires an Adept Scientist. This is the place just left of the research place. You will see round broken table here. To restore it you must take five objects back to this place. The objects are scattered in the village. They can be hidden anywhere but are very distinct. The objects are a mud pot, a blue bowl with spoons kept in it, a small striped Pink Pot, a large striped blue pot, and a knife. Once all objects are placed back you can prepare different recipes. Note: Only an adept scientist can collect these objects and automatically place it at the alchemy lab.

Puzzle 4 - The Roster Of Dead: Fly a villager to the right-most end of the empty ground just below the mud place (orchard). You will find something covered with leaves. Allow your villager to remove the leaves. You can now bury the dead here.

Puzzle 5 - Weather Dancing: You will need level 2 Leadership, a Tribal Chief, and three Adept Farmers. First, drop the chief on your lit fire. He or she will begin weather dancing. Then, drop the farmers on the fire and they will join in. You will know they are successful when sparkles appear over their heads and under their feet.

Puzzle 6 - The Lift: This requires level 1 Restoration. In the mud place you will see a broken see-saw type of object. Let three of your builders work simultaneously on the broken object. They will fix it.

Puzzle 7 - The Ruins: This requires level 2 Restoration. Scroll down the village until you see a broken bath tub. In that area you will find a pile of stones. Place a villager on it will and they will start removing the stones. Once removed you will find the hidden cave.

Puzzle 8 - The Ancient Bath: This requires level 2 Restoration and Master Builders. Put the Master Builders in the Alchemy Lab near the chalkboard. It will draw something on it. After that, put the builders on the broken bathtub. They will start repairing it.

Puzzle 9 - The Statue: This requires level 3 Restoration, Tribal Chief, and Master Builder. Put the Master Builder near the standing half of the statue on the route to the locked door. Just fly it over that area where it says that it is a nice place to anchor the statue. Put the villagers at that location. It will prepare to anchor the broken statue. Immediately also put the Tribal Chief at that location. Then, put as many builders possible near the fallen statue. The more builders, the sooner they will anchor the fallen piece. During this time do not disturb the Tribal Chief or the builders will become distracted.

Puzzle 10 - The Orchard: This requires Puzzle 3 to be solved. To complete this puzzle you must plant three seeds at the orchard (the mud place). One seed is present at the start of the game. For the others you must wait for the rain. When it rains, put a villager on the flat end of the lift. As the water fills the other end the flat end will rise. As it rises fully a seed will fall. Put the villager over the seed. It will plant it same way as the first one. Do the same thing for the third seed. After a tree grows from the all three seeds the puzzle will be solved.

Puzzle 11 - The Sharks: Requires Level 2 Alchemy and Level 2 Natural/Magic Faction. Create a potion using one Pitcher/Berry Plant, two Rose Plant. You can tell a potion is correct when there is a sparkle emerging in the steam from the cauldron. Place a Villager on the alchemy pot and they will take a vile of the potion to the sea. The potion tames the sharks and allows you to fish in the ocean without danger. Fishing is an unlimited food source.

Puzzle 12 - Aromatherapy: You will need to have completed Puzzle 8, have level 3 Medicine, and a Master Doctor. Drop your Master Doctor in the completed bath. He or she will fill the bowls around the bath with Lotus plants (doing aromatherapy). Then, drop a Master Doctor on the fire to light the burners and finish the puzzle.

Puzzle 13 - The Ash Key: Keep burning the fire at the village center. After one or two re-firings, a sparkle thing will appear on the burning fire. Wait for fire to get over. Once it gets over you will see the diamond. It is hot. To cool it, put a villager near the waterfall. They will bring water and pour it on the diamond. Repeat this five or six times. Once it has cooled, put the Tribal Chief on the diamond. It will carry it to the locked door.

Puzzle 14 - The Cliff Key (the diamond key): Prepare a potion with Cactus, Rose Plant and Lotus. Let a villager drink it. They will feel light and springy. Place it near the rose plant, to the left of it. It will retrieve the key.

Puzzle 15 - The Clam Key: This requires Puzzle 9 to have been completed, a Master Builder, and Tribal Chief. Once the statue is built, you will find a white sparkling object below it. Let your Master Builder collect it. He will take it near the waterfall and carve a pearl out of it. Put your tribal chief on the pearl to finish it and mount it on the locked door.

Puzzle 16 - The Chief And The Princess: Once the locked door is opened you will see a flat blue plate inside the room. Put your Tribal Chief on that plate. The souls will appear. Putting the chief on the souls will retrieve the story of this ruined ISOLA.