Well, there isn't much to say honestly. I greet them when I see them (aside from my grandfather and any others who have passed on).
I speak to my grandpa when I think of him, often when I see classic cars, as his greatest passion was restoring them.
Often, I am expressing gratitude for lessons taught, for the air I breathe, for the food I eat...
When I consume food, I thank the plant or animal that it came from, and the Earth for it's bounty.
A lot of it is the recognition that I am part of the great web of Nature.
I rely on trees and plants, and they on me. Similarly, my animal friends and I rely on each other for comfort and companionship (and food and water on their end).
Like Carlita said, I do speak to the Earth on equal terms, and with reverence. While I revere and even choose to personify Her at times, I also recognize that I am not truly separate from the Earth.
I am a part of the web of life, just like the rest of the earth.
As a side note: I am also an ex-Christian, and towards the end of my Christian "walk" I began to speak with my God on more and more equal terms (though with no less reverence). I now call It Tao, and view it in an extremely different manner.
Thank you, I like it too. I find it to be comforting, and it serves to constantly remind me of our interconnectedness.
Also, I really like that image you posted! I hold the position that everything is Natural. There is no "supernatural".
On the other hand, you could just as well call everything supernatural and say there is no "Natural"...I do not discount some things that would traditionally be called supernatural, but I believe that everything is a part of the Universe and Nature. Therefore, everything is Natural.