DJ Delorie replies: The most reliable easy way is to chuck a length of wood into it, and turn on the lathe at low speed. You’ll be able to see the center of rotation on the free end, and decide if it needs further adjustment.
However, you can also experiment with various “push here” techniques to see if one of them just works. For example, on my lathe, the back edge of the slot guide is properly aligned, so if I push the headstock away from me while tightening, it tends to be properly aligned.
You can also purchase alignment jigs, like a rod with a Morse #2 taper on both ends, to help align the headstock to the tailstock. If you happen to have a pen turning mandrel, or three-buff mandrel, those can be used as well. In that case, there’s often no need to turn the lathe on if the mandrels are accurate enough and properly seated in the taper.
Jon Siegel replies: A special tool is available for this. It is a metal rod with a Morse taper at each end. Just insert it in the headstock, and bring the tailstock up until the tool fits into both tapers – Packard Woodworks #113121 – $16.95.
But you do not necessarily have to buy a new tool. You may already own a drill chuck on a taper shank or a bowl chuck. If you do, then place it in the headstock and chuck a metal rod (or a thick wood dowel) about one foot long into the chuck. Run the lathe at very low speed and you will be able to find the true center even if there are errors in the straightness or the chucking of the rod. Bring the tailstock up close to the end of the rod and adjust the headstock until the rod is centered.