There are several tutorials on this subject. I suggest you try to read them all. Answers to your questions should be found there. However, in the spirit of this forum, I will offer this as the way I do what you are asking.
1) Using a 4" long by 1¼"/Sq blank, I drill a ¼" hole all the way to my desired depth - 3½"
2) To turn, I place the blank on a ¼" x 5" long bolt in my collet set up. I use a couple rubber washers at the collet end of the bolt to aide in holding the blank from slipping.
3) Turn to shape. Everything should come to "center" if your machine is set up correctly and your ¼" hole was drilled half way straight.
I do all my drilling on the lathe. The method I use is similar to other methods already posted in the tutorials I mentioned. There are different ways to do this and they all are designed to get to the same end result. You'll have to put in a little research, do some reading and experimenting, and find what works best for you.