I have a pair of buttons that I use to align my tailstock well enough for most purposes. It is basically a pair of flat buttons cut at the same time so their OD'S are identical. Then they are drilled through and then chamfered to a 60 degree taper. The chamfer must be done by cutting it not by drilling it with a center drill.
In use, you put one center in the chuck and one in the tailstock and pinch the two buttons together with both centers. You can easily use your fingers or a micrometer to feel, see, and measure how much your tailstock is off.
Just like a lathe center standard, these buttons are a great project for new lathe owners.
Edit - here is a link to some buttons that are quite similar to mine. The author does a great job of describing how to make them. Mine are not as long as these are. I think that shorter buttons help to magnify any difference in alignment.
Proper alignment of the tailstock axis to the lathe spindle axis is essential to parallel turning on the lathe. Horizontal alignment is far more
www.homemadetools.net