One of the advantages to drilling ona lathe as compared to the drill press, is that the natural tendency of the bit is to pull towards the center of the work piece (path of least resistance) - of course, all sorts of outside factors come into play, but with some effort - its easier to get a centered hole on a lathe than it is a drill press.
Like Jester said, Start you hole - with a very short bit so it doesnt wobble. Like a center drill or spot drill.
For the most centered hole, your tailstock needs to be centered too - but I have found on wood lathes.... yeah good luck with that. So, the goal is to be as centered as you can. With that short bit (center drill or spot drill) and the part in the collet - face off for a nice flat surface. Then move the bit up to the face, and SLOWLY just barely touch the face... if its centered, youll see it, if its not, youll see the tip cut a faint circle. Back off, loosen the tail stock, re adjust it, and try again, get it as close to center as you can.
Once its as close as you can get it. Move the bit in very slowly. What you are doing is starting the hole, and it wont be very deep. Personally Id suggest a spot drill the same size as your regular drill so you are creating a "guide" for the longer bit. But a center drill will give you an angled start which is very workable.
Once youve gone in with the spot drill to at least 3/8" you can back out and change bits. If you use a center drill, only go in far enough to get the taper of the drill part way in. You dont want the taper left to be larger than the drill youll be switching to. Also, go slow! You want that drill to actually act a little like a lathe tool... youre really drilling, but if the bit is off center, it will cut on the side a little. You want it to do that, its creating a centered location.
Now when youve switched to the longer bit - if you used a same size spot drill, just line up and start drilling. Too slow a feed and you will get chatter, to fast and you risk the bit being pulled or pushed off center, either by drill flex or grain soft spots - its a "Feel" thing - it will take a little practice. If you used the center drill, start the drill VERY slowly.... you want those leading flutes to cut a little more like a lathe tool than a drill. This is where the physics come in, if you go slow enough, and the bit is off center at all, it will cut the hole just a touch bigger than normal. But as you feed, the edges on the side of the drill arent shapped for cutting, so they wont cut so much, and they will push the drill to the center. Once you have that going for a little ways, you can speed up your feed, just not too fast. You want to keep the drill in motion. Stopping the drills movement will cause issues. If youre not feeding in, you want to be feeding out - not standing still. I will usually start with the tail stock clamped and feed from the hand wheel. Once Ive gone in as far as I can, back the drill out, then Ill unclamp the tail stock, and just use the "Arm Strong" power feed method :D but be careful to not feed the drill to fast, and clean the flutes regularly.
Hope that makes sense... :D
Wade
