Lathe Head stock or spindle Alignment
Check spindle alignment by chucking up a piece of material and performing a cut. The material should be a minimum diameter of 2" and around 9" in length. You only want about 6" extended from the face of the chuck jaws. If the diameter of the material is too small or the material is too soft, it could deflect. Unless you want to perform an alignment twice. Once the material is chucked up safely, make a program to turn a 6" length and start cutting. Make sure the cuts are not too heavy, and make sure to clean up the part completely.
Then, measure the piece with a micrometer at both ends. The readings generally should be under .0004" of each other, but check with the builder for their specs. More tolerance may be acceptable depending on what parts are made on the machine. If the chuck side is larger, then your spindle is tilted up towards the upper turret. If the chuck side is smaller, then your spindle is tilted down. Before adjusting anything mount an indicator on the end of the bar and record the reading.
As far as performing the spindle head alignment. This can be fun. Most headstocks have two sets of push pull screws and 6 to 8 Large bolts used to lock down the headstock. First I would tighten the push pull screws down tight opposing each other, but not too tight that you strip them out or bend the bolts. Then I would loosen the hold down bolts. The push pull screws will hold the headstock in relatively the same place. Read your indicator and adjust the push pull screws to jog the head around. Use your indicator to make an estimate as too how much you should move it. Then tighten bolts, no need to really crank them down yet. Now take another test cut and repeat above until you are within tolerance. I like to get it under .0002".
Once you are within tolerance don't forget to crank down the bolts and take one more test cut to make sure it stayed within tolerance. Then loosen push pull screws a little so they do not get damaged in the event of a crash.