Here are a few pictures of the construction and the finished island.
Note: Everything was built in survival mode. All items are mined by me. No spawned stuff used.
As for the first island, I start off by building a path to the building site.
This is the look to the first island from the building path.
Fell off the path, this is the view from the water.
Climbed back up and started building the top layer for the second island.
Started filling it in.
Got it finished.
Next, I built a bridge from the first island. That way I could access items, that I stored on the first island.
This path next to the bridge is used to transfer some grass on the second island.
The grass starts to grow to the second island.
View from the path.
View from under the top layer of the second island. To the left we can see the bridge to the first island.
Started building the next layer made of stone (clean).
Filling the first stone layer.
Got knocked down by a zombie, took this screenshot :D
Climbed back up, went on building. We now started the second stone layer.
Got most of the layers finished. The dirt thingy you can see under the bridge was used to get up to the bridge because the path from the mainland (under the island) ended under the island and I couldn't climbe up to the island.
Grass keeps growing.
Some time later, grass reaches the island and starts spreading.
Finished the stone layers. Now destroying the path to the mainland, because I can access the island from the first island (swim up the waterfall and walk over the bridge).
Waiting for the grass to grow...
Grass finally finished (took some time -_-).
Destroying the grass path.
Building a fence so the animals can't get out.
Trees have grown.
Had to rebuild the dirt path to the mainland so I could get the animals to the island (used wheat :D). Animals are now captured.
View from the first island.
Now heading back to the mainland. This is the view from the boat.