When I was throwing the other day I was trying to quantify and qualify what the whole process was all about. One of the things that struck me that may confuse beginner potters is that when you are wheel wedging (when you make the towering cone) it is easy to think that what you are doing is pulling the clay up. You really aren't. You are pushing in and this forces the clay up which you follow as you push in. If you have on a bat, you can tell you are doing it wrong if the bat is flopping on the wheel because you are pulling up and not pushing in.
When you push this cone down, some of us have been taught to bend the cone over and follow it down. This makes pushing down much easier for very large pieces of clay but for small pieces it is needless and actually can throw it off center some. Just push directly down or bend only slightly to the side and follow down to the center.
Once the wheel wedging is done (the clay feels close to center, nice and smooth and more 'giving') 'centering' is done for both the shape (flat or high - a filled donut shape) and having the clay centered. This actually calls for a very light touch since most of the 'hard' centering is done with the wedging. Once you have it the shape you want then it is simply a very light and immobile touch until all feels right to the world. If it feels like it is going off center lighten your touch. GENTLY remove your hands. Indent the center and open to the floor.
I now only open the floor that amount which is going to be entirely flat (unless it is a large pitcher, vase or plate this is typically only an inch or two. I then reinforce the rim and even out the walls (which at this stage have a C shape - changed to more of a L). Now I use the rib to form the bottom curve if the shape is a bowl. Reinforce the rim again and start pulling. Pulling is actually what it looks like and not what is going on in my feel of things. You are having equal pressure of pushing in, pushing out and following up.
The speed of the wheel is important in each of these processes. If things don't feel easy, adjust the speed. I have the wheel fastest at the beginning and the slow down as I progress.
Don't know if that makes sense to anyone but thought I would throw it out for consumption. DK