I understand your question to be, how do you create a logo with the golden ratio? I feel as if your question is more theoretical than program based? Here is my theoretical answer and I will be the Devil's Advocate for the golden ratio here (as I believe many of the comments above don't completely understand the significance).
Sketch on paper. That's how the best logo's start. Do NOT try to create the above schematic and fit a logo into it. As other's have said, these images you have above are more for marketing than they are how the designer actually created them.
After you have your base idea (IE: using the Twitter logo, let's say you know you want your logo to be a bird and you've sketched the basic shape of the Twitter logo) you can bring the sketch into Illustrator and begin doing the math. (IE: making sure it fits the golden ratio).
You do not need to create this type of "grid" as you see in these photos and than fit the logo into it. Instead, you need to understand what the golden ratio is and how it can assist you. When you know how you want it to assist you, you can start doing the math.
We'll use Twitter as an example. What we're looking at in this one is the size of the circles (that is what is important). This "golden rectangle" you're seeing everywhere is actually the Fibonacci Sequence of numbers (you'll also see it with a spiral, which is what many artists use to create a directional eye flow in their pieces). So you see the "main", large circle here is the size of the bird's body. Or, at least, the bottom of the bird's body is following the curve of this circle. This is the main diameter (width) we'll be utilizing to use the golden ratio to get the size of the bird's wings, feathers and head based off of the size of his body.
To SHOW you the relationship between the objects the designers have placed the Twitter bird into that golden rectangle we talked about. I, too, have a shape file in Photoshop and Illustrator to help measure with the golden ratio. HOWEVER, what they more likely did, was took the circumference of the bird's body and divided it by 1.6. 1.6 is the rounded golden ratio number. But visually, what this actually does, is makes the second smallest circle that you see the correct size in relation to the first, larger circle.
"Why does this matter? Why not just make a smaller circle and call it a day?" The answer is because everything comes down to the way our brains perceive the world around us. Naturally beautiful things--many things found in nature--have a size or spatial relationship utilizing this ratio. This means, our brains are more likely going to subconsciously recognize these relationships as beautiful. I have not yet had an instance where I utilized this relationship correctly prove that statement or philosophy ineffective. As a secondary benefit, if