First of all, forget "absolutely dead center" -- that term is incompatible
with a drill press. A drill press is a tool for rapidly putting holes within
a reasonable tolerance of where you want them. That being said, this problem
breaks down as:

1) making the hole start directly under the spindle axis (i.e. preventing drill
bit wander) which is done by centerpunching and also by using very rigid drill
bits known as "center drills" which you can get at http://www.mscindustrial.com

2) putting your centerpunch mark exactly where you want it which is easy to
do within ten thousandths but very hard to do closer than two thousandths. This
is done for high precision by the use of an optical center punch.

Holes that have to be very precisely located aren't drilled, they are bored.
The machine that does this is a jig borer.

Most woodworking tolerances are on the order of .010" so you can probably
get away with learning to do layout and centerpunching. Once you have a
centerpunched mark, then it's also tricky to get it lined up exactly under
the machine's axis.

All of this supposes that your drill press table is at precisely right angle
to the spindle axis, and that your drill chuck has zero runout, neither of
which is likely true, especially if you're using something you bought at
Home Depot.

GWE

Doc wrote:

Looking for any tips/tricks for drilling a hole w/a drill press that's as
close to dead-center to a specified point as possible.

Here's what I've been doing - I have the position marked with graph paper
that's taped to the workpiece. With the help of a magnifying glass, I
painstakingly move the piece until the tip of the bit is aligned with the
conjoining lines. By aligning with the tip I mean I view the tip both from
the narrow or "pointy" persepective within the channel of the bit and then
turn it 90 deg and look at the the wider perspective, and view it from the
side and front to make sure I have it aligned with both the X and Y axis.
When I finally get it so the tip is as centered as I can make it whichever
way the bit is turned and in relation to both axis, I clamp the piece to the
plate of the drill press and drill the hole. However, on examination, the
hole comes out obviously not dead center in relation to the graph paper
lines.

I've also tried aliging it with the drill running, going visually by where
the "point" appears to be when the bit is spinning. I get somewhat better
results this way but wonder if there's a more precise and dependable way of
achieving a centered hole.

Thanks for any input.