The Aztec floating garden looks like a floating garden. 
In reality, it is a garden that is supported by pylons.  The picture on the left is a drawing of an Aztec floating garden called a Chinampas.  The benefits of growing a Chinampas garden are: they provide shelter for the pond fish against predators, and vegetables grow healthier and yield 7 times more crops.

Here is a modern day Chinampas constructed in a grander scale than the one we will make for the backyard.

Step 1
Start with vines and saplings and build a square frame. Fasten the cross pieces of the frame with twine twine (I used zip ties).  Layout rows of saplings vertically and tie down.  Weave the vines horizontally across.  Tuck in extra pieces of vine and wrap vines around the edges of the frame.  This might look like a tangled mess, but it looks so much better in person.  All this is is a simple crisscross pattern - horizontal / vertical pattern - over under.  I used the left over short pieces to fill in a few holes. 

Step 2
 
Palm Tree Frawns were used to cover the woven grape vines and tied down with twine.  If you do not have access to a palm tree, then banana tree leaves or bird of paradise will work well too.  If you do not have access to these, straw is your next option.

Step 3

I used 2 cinder blocks to hold the mat above the water, but a traditional Aztec garden uses steaks or pylons driven down into the muddy water below. 

Step 4

Add a layer of cured compost on top of the chinampas and plant your seeds or plants.  It's okay if a little compost falls into the water.  I planted mint and parsley in this garden.  When it takes off, the entire platform will be covered.  

This garden is 3 foot square.  If I built another garden, I would make an edge around the sides to keep the soil boxed in.  The traditional Aztec garden, however, is flat and much larger than this one.