Sometimes it's difficult to come up with good names for things. I call this step turning the stitch, but I don't know if there's a real name for it.
What you're doing is sliding the right-hand needle from the back to the front of the left-hand needle, keeping the loop of yarn on the left-hand needle for now but punching through with the working yarn so that it makes a loop on the right-hand needle.
To do this, just slide the right-hand needle down so that the loop gets close to the tip of the needle but doesn't slide off. When the tip of the needle gets close to the edge of the left-handle needle, give the right-hand needle a little push so it can move in front of the left-hand needle. That's the "turn" I was talking about.
When you get to this point, it all starts to make sense and look like you're actually doing something. Congratulations!