Mars,
Post a picture of your lathe. Some of the guys here know these machines inside and out. The things you learn when setting up and cutting become inherently obvious after awhile.
Generally the watchword is "ridgidity". Just before you start a cut, stand back and look at the tool set-up. What you are looking for is a straight line of force down from the point of the tool to the bed ways. If your tool set-up diverts the path of force too much, you will introduce the risk of chatter. Additionally, the hardness of the material being cut can cause chatter. The ridgidity of the material being cut is also a consideration. A two-inch diameter bar of steel is a lot less likely to chatter than a one-inch piece.
There are things you can do to help preclude the risk of chatter as you set up your tooling. One is to adjust the gibs on your cross-slide and tool post slides to eliminate as much slop as is reasonable. I.E. you don't want to work too hard turning the cranks on both, plus it prematurely wears out the lead screws.
Some of the old lathes were equipped with the Armstrong tool holders for high speed steel. These are ok, but are not as ridgid as some of the newer tool holding rigs. I. E. the Aloris style tool holding system.
The sharpness of your tool and the angle the cutting edge presents to the material being cut can introduce the risk of chatter and other vibration. Generally, you want the chip to slide away from the tool as the cut is made, otherwise the tool bit will heat and fuse cut material to the cutting edge and leave a poor finish on your work.
If you could find a hands-on machinist class somewhere locally as well as taking advantage of Glenn's offer, you will be generating chips without serious problems before you know it.
Finally, verify that your machine is level and each point of contact with the floor is carrying its alotted load. I.E. if one or more of the leveling adjustments is loose or not set correctly, your lathe will sing like a banshee. WWQ