Proper alignment of the tailstock axis to the lathe spindle axis is essential to parallel turning on the lathe. Horizontal alignment is far more important than vertical and that is why most tailstocks are fitted with a mechanism for moving the axis horizontally but have no vertical adjustment.
There are numerous ways to calibrate alignment but a simple and effective way is to use alignment buttons, which you can make yourself on the lathe. Let's discuss the tools and their use first and then I'll comment on how to construct them.
The two buttons look like this...
The larger diameter portions are precisely the same diameter.
They have center holes on the smaller diameter ends like this...
In use, the two buttons are mounted between centers using the center holes and the larger diameter parts face-to-face. Now, if the tailstock is misaligned the buttons won't quite align radially. A micrometer placed across the line where they join will show a reading larger than the diameter of the buttons.
One adjusts the tailstock setover until the micrometer reading across the join line is the same as the large diameter. When this is true the tailstock is aligned.
Now, how to make them...
To ensure that the measurement buttons are the same diameter, make the buttons as one piece. Take a piece of stock and center in a 4jaw. Turn down one end and center drill. Reverse in the chuck and recenter, then turn down the other end and center drill. Turn the larger diameter center section.
Cut the piece in half and face the cut ends and you've got your tool.
Lots of folks, myself included, are reluctant to go through the hassle of chuck removal and center mounting to turn a piece between centers.
Leave the 3jaw in place. Put a piece of steel in it and turn a 60 deg point on it by angling the compound rest. As long as you don't remove it and replace it, this center will be as accurate, perhaps more accurate, than the supplied headstock center.
With the chuck jaws there, fabricating a dog to drive the workpiece gets easy. Many times I've drilled a hole in a waste area and inserted a pin long enough to bear on the chuck jaw.