Get a center finder- used to use them in machining all the time--
simply a 1/4" rod with a 30 degree cone machined on one end. Helps to
center punch the center of the hole on the workpiece first, as the
indentation will provide an easy physical reference for the end of the
finder.
Chuck it in the drill press
Find the center of your drill hole- you may want to lock the quill at
this point
Clamp the work to the table-- unlock the quill
Change out the center finder with the bit you will use
Drill