John, even a not so great machine is better than a file, vise and hand drill I think we all agree. I was going to just watch until you asked for more help so here we go. There are things that can improve even cheaper equipment to bring them more to the tolerances we can live with.
First thing is to put something like a dowel pin, you can get one from McMaster here, in the chuck to check the concentricity of the spindle. Indicate it in so it runs true (bumping will/may be required of the jaws-tighten more as you get closer to zero). If you can not get it to zero movement on the indicator, write down the dim. This will be the concentricity that you can expect to hold. If the spindle has slop in the main bearings causing excess movement you might be able to fix it by staking the spindle where it engages the bearings, using loctite to take up the gap or tighten compression sleeve if so equipped. Knowing how close the concentricity you can achieve is important. Keep in mind, this is from the work holding to the cut diameters. If you are cutting two or more diameters with the same work holding the concentricity between those may be better.
Second thing: Move the indicator out to the end of the dowel pin and indicate it to zero or as close as you can. If it will not zero out make sure the run out is the same near the chuck and at the far end. (It would be a better idea to do this for the first step as well) When this is running true as you spin the chuck run the saddle/carriage back and forth from both ends with the indicator in the center of the pin. If you get anything except zero write down the dim. This will produce a taper twice the measurement because you are only measuring one side of the diameter. If the head is bolted to the bed, loosen those bolts and bump the head until you get as close to zero as you can get. If the machine had square ways this may be much more difficult to dial in than with the "V" ground ways (Much preferred). If there is play in the saddle find the adjustment screws to take out the excess slop and try again. By the way, the cross slide and compound slide should be locked into position so you can eliminate those moving while you check the straightness.
-----Another check here would be to put the indicator on the top of the dowel pin to see if it is parallel to the ways. If not, write that dims down as well.
Next you will need to check that the cross slide actually moves 90 degrees to the spindle center line for facing. One way, not the only way, is to clamp a precision sqaure to the dowel pin. Put the indicator on the edge of the square and move the cross slide back and forth. Here you are at the mercy of the ways unless it is a square way machine. If the indicator moves showing out of square and the machine does have square ways you can/ should be able to adjust the screws to rotate the saddle/carriage back to square. Get this as close to square as you can. If the machine has a "V" ground way your are pretty much stuck with what you have without some extra work in a Bridgeport to correct it.
Check the compound angle. Indicate the pin to zero while bumping the compound parallel with the pin. Verify the register mark is on zero. If not, make a new mark. Locate the opposite end of the angle scale on the compound and verify the register mark is good there.
Center the Tail Stock. Two methods here. 1) put the indicator in the chuck and spin in the bore of the tail stock spindle while the tail stock bed and spindle locks are secure. Bump the tail stock in or out until it zeros. Front and back being zero is more import then up and down. Both would be great. If the spindle center line is high, the base of the tail stock could be machined to bring it down to center line. If it is low, you are kind of stuck without maybe plating the bottom of the tail stock and having it ground back to center line.
2) Get a ground shaft, Thompson rod is good, at a length that would be the longest distance from a center in both the chuck and the tail stock. The Thompson rod should be small enough in diameter to fit down the headstock spindle (7/8 or 3/4"should be good, check to be sure). Put Thompson shaft into chuck. Indicate it to zero run out. Center drill and drill a 1/4" hole about 3/8 deep. Set the compound on 30 degrees and cut a true surface for a live or dead center, about 3/16" long. Do the same on the other end of the Thompson rod. Now make a dead center for the chuck (google search images), put a dead or live center (dead is most likely more accurate) in the tail stock. Put the rod between centers with light pressure from the tail stock. Indicate the shaft from one end to the other. Offset tail stock as needed.
These few things will dial in to the best you can hope for on any lathe. While there may be more than my way to get there, these are proven.
this info will come in handy
