There is a couple of ways you can do this. I made an arbor for ball turning. It is a small diameter shaft that is threaded at one end for what ever thread size I am making the ball for. First I take a piece of round stock the diameter I want the ball, insert the rod in the chuck drill and tap the rod then cut the rod to length (for example if you turning a 3/4 inch ball cut the rod 3/4 x 3/4), thread this section of rod. Let the arbor stick out from the chuck a bit and you can start turning. It takes a little time you want to remove only a few thousands at a time. You will be sweeping the cutter from front to rear. It will start to take shape in a short while. You get the feel for it as you work. You will have to touch up the turn on the chuck end because you can only turn so far.
The other way is to turn the end of the rod you have just drilled and taped to a round shape once this end is done cut the rod to length and thread the drilled and taped end on to the arbor then turn the back side.
I'm sure there are other ways to do the job but this is the way I do it. Hope this helps..