I think I understand where your problem lies. You need to understand the basics of what you're doing.
As the article say, you're making a series of paired cow hitches. Each pair is started with one part or the rope, and then finished with the other, alternating back and forth.
Teh "steps a-e" in step one, are an explaination of how to tie a cow hitch. Most people know the simple way, make a bight, loop it around an object, and pull the "tails" through the bight. Not always an available way to do it. Steps a-e show another method.
Basically, take your rope over the pencil and drop it down behind. Bring the part behind the pencil forward, and cross over the rope in front of the pencil. Now bring it up behind the pencil again, and then bring it forward, down in front of the pencil, but behind that part that crosses over the rope, essentially between the pencil and the 'crossing' part of the rope.
With Step two, you're treating the bight of the first cow hitch, as if it were the pencil, anyou tie a cow hitch around it, using one side, in this case, the left side. In step three, you are repeating the process with the other strand, the right one.