Detailed spoilers for the 16 puzzles:
(courtesy of ladycfii)

Don’t read these unless you want to know exactly how to solve each of the puzzles.

Puzzle 1 requires a builder to clean up the well, so that there will be a source of fresh water for your tribe. Drag a villager with some building skill to the well.

Puzzle 2 is the first of 3 additional huts that your villagers will construct as your population grows and your villagers require more housing. The huts will be initiated, as needed, by one of your builders. Your population is limited to 7 villagers until the first hut is finished. Once it’s finished, your tribe can grow to a population of 15. The second hut allows your population to expand to 30 villagers, and the final hut allows your population to grow to the population limit of approximately 90 villagers. You must have a villager trained in building in order to build the new huts. At the start of the game, one of your builders already has skill in building and will work on the hut unless you retrain them and assign them to a different occupation. It’s important to make sure that you have at least one builder in your village so that you will be able to provide additional housing for your growing tribe. If none of your villagers has any skill in building, and you need to train a builder, your villagers can gain building skill by fixing any of the 3 huts that they have constructed.

Puzzle 3 is completed by cleaning up the debris on the beach. Completion of this puzzle is required before your villagers will be able to fish in the ocean (which also requires Level 3 of Farming). Drag a villager to the debris field and they will begin cleaning up the beach.

Puzzle 4 is the founding of a school for your village. Drag a master scientist to the long building north of the research table.

Puzzle 5 is completed by removing the blockage from the creek in the northwest corner of the village. Your villagers will need to have researched Level 2 of Construction to work on this puzzle. Drag a villager to the pile of rocks blocking the flow of water from the creek. Once the blockage is cleared, the water will flow into a sparkling lagoon that your villagers will use for various work and leisure activities. This puzzle is a key to three other puzzles.

Puzzle 6 is dependent upon the completion of the lagoon and level 3 of Farming. Take a master farmer to the lagoon, and they will begin hunting a strange fish (this is not the way your villagers fish for food - this fish is the Fish of Fertility). It may take many tries before they succeed, so be patient and keep trying.

Puzzle 7 is the discovery of the graveyard and requires Level 2 of Spirituality to complete. When one of your villagers dies, drag an adult villager to the northeast corner of the island. The villagers will celebrate the discovery and will then proceed to provide a proper burial for that little pile of bones in village center. After the first burial, your villagers will initiate burials for all deceased members of the tribe.

Puzzle 8 requires that your villagers master the medicinal properties of 4 plants indigenous to the island. One plant is located south of the lagoon site, one is the cactus that’s located near the boulder, and the other two are on the east side of the island. Drag a villager to each of the 4 plants until each one is mastered.

Puzzle 9 is dependent upon the completion of the lagoon. Take one of your villagers to the field on the east side of the island (where they see dead flowers), and they will begin to water the field with the pure water from the lagoon. If you have builders in your tribe, they will begin to water the field on their own. Villagers without building skill will water the field, also, but will stop after one trip. Once your villagers have put sufficient water on the field (it takes a lot of water), the field will be revived and will once again be in full bloom.

Puzzle 10 is dependent upon the butterflies from puzzle 14. Those butterflies will be able to pollinate a special plant on the island. Once the butterflies begin to follow the Golden Child, drag him or her to the strange plant north of the berry bush.

Puzzle 11 is the restoration of the temple at the site of the ruins. After attaining Level 2 of Spirituality and Level 3 of Construction, drag one of your villagers to the ruins in the southeast portion of the island, and they will begin restoring the ruins.

Puzzle 12 is dependent upon the completion of the temple, as well as attaining Level 3 of Spirituality. Drag one of your builders to the sparkly rock on the west side of the village, and they will begin to chisel the rock.

Puzzle 13 is the birth of the Golden Child and requires the completion of the idol, the lagoon, and Level 3 in Fertility. You will need to take a nursing mom to the lagoon.

Puzzle 14 is dependent upon the Golden Child. Take the Golden Child to the Magic Flower Garden.

Puzzle 15 is a buried treasure. Its location can be discovered only by an adult master builder. Your tribe must also have researched Level 3 in both Construction and Science before they have the technology required to make the discovery. You must actually drop your builder in the right location - dragging him around won't help you find it. Look for the message, "Is something buried here?" to tell you that you're in the right place. If you want a hint for the location, highlight the following invisible text: Try dropping your builder in various sandy places in the lower half of the village map to see if he notices anything. If you want the exact location, highlight this text: Try dropping your builder directly south of the food bin in line with the temple. Once he locates something, you may have to be persistent before he will actually start digging. Keep dropping him there - it could take many, many tries. Once he starts digging, and the scaffolding appears, other builders (if you have any), regardless of skill, will start to help, too!

Puzzle 16 is the moving of the boulder, which can be done only by the Golden Child. You don't need to make him do anything (and it won't work if you try). Just give it some time, and he will take care of it for you. After he’s born, you should just watch him for a while, if you have the time - it's entertaining to see him solve that puzzle, especially when you have a lot of villagers.