Parting seems to be difficult for almost everyone, including me, until you learn the "secrets" (which are really simple steps that must be followed to a "T" in order to be successful.) I respectfully disagree with those that say parting cannot be accomplished on a small lathe. I have successfully performed parting on my 1943 Logan 10" lathe as well as my dad's old worn Atlas 10" bench lathe, a model which many say is not very rigid. On both lathes I have been able to reliably part by both hand and power feed. I am an amateur machinist with no claim to expertise, however these are the keys to success for me:
#1 Rigidity of the work. The cut should be made as close to the chuck jaws as possible. Certainly no more than two diameters of the work away from the chuck jaws. Closer is preferable. DO NOT attempt to part between centers in an attempt to achieve rigidity. You will likely break your parting tool toward the end of the cut or damage the work..
#2 Rigidity: If the chuck's jaws are bell mouthed you cannot maintain rigidity of the work, no matter who much you tighten the chuck jaws. If you are using a lathe with a threaded spindle be certain there are no chips in the threads of the spindle or the back plate and of proper fit between the spindle shoulder and the chuck back plate. There should be full contact at those points if the backplate is properly fitted. Blue those areas and install the chuck then remove and look for blue that has not been removed. Those are areas with no contact, correct the fit. The portion of the spindle shoulder I speak of is the one that the back plate butts against, not area that enters the backplate bore. (Without getting into a huge debate about how back plate bores should fit the spindle I'll say that I subscribe to the belief that the threads, due to their 60 degree form, center the chuck on the spindle to prevent runout and that the shoulder the backplate butts against holds the chuck true to the axis of the lathe ways. Others may disagree, and that is fine, but that debate is like debates on which oil is best, circular and without end.)
#3 Rigidity: The tooling must be set up as rigidly as possible. If you are using a Lantern tool post ditch the rocker and make a solid steel ring of a thickness that puts the tip of the parting tool on center. With a QC tool post be certain there are no chips under the tool post and that it fits the compound flat without rocking. Compounds can have worn surfaces from years of use that will not allow tool posts to be rigidly mounted. Dings from dropped tooling will cause raised areas that allow minute rocking and ultimately chatter. Be certain that the parting tool does not extend any further from the holder than is necessary regardless of what tool post you use. If using a Lantern tool post choke up on the tool holder as much as possible. Keep overhang to a bare minimum.
#4 Rigidity: Think about every possible way for movement to creep into your setup and eliminate it as much as possible. Properly adjusted machine gibs, small tool overhang, tight tool posts, holders etc. Be certain your headstock bearings are properly adjusted if they are plain type or have proper preload if of ball type.
Up to this point most of what has been said is appropriate for accurate chatter free plain turning and boring as well as cutting off. Much is just general good practice for machine maintenance.
#5 Parting tool alignment. The parting blade must be perfectly perpendicular to the work and on center. Take great care in assuring this. I usually use the lathe chuck as my guide and put the parting bit right up against it. I use a white piece of paper or a light shined from below to adjust the tool holder/post until the light coming through shows an equal space at the blade tip and where it meets the holder at the outer perimeter of the chuck. I use the same care I would when I set up a threading tool for a threading operation using a Center Gauge. The parting tool must also be perfectly vertical. If it leans one way or the other it will rub on one side and track to the other.
#6 No back rake on the parting blade itself. It should be on centerline of the work and level. Be certain there is adequate front clearance or the tool will rub rather than cut and of course there should be side clearance on both sides of the blade. If the cross feed requires much pressure when attempting to part be certain to check front clearance, the tool is most likely rubbing due to lack of front clearance or is adjusted above center. The blade should be sharp and honed to a fine edge at the tip and sides. Some advise grinding the tip at a slight angle to eliminate the tit left on the work. I do not do this as it seems to make the narrow parting blades I use try to wander to one side. I grind my tip so it is perfectly parallel to the work.
#7 Once you have the cutoff tool position where you want the cut lock the carriage to the ways.
#8 Speed. I generally use speeds of about 1/2 to 2/3 that recommended for turning whatever material I am parting. Don't be afraid to try a faster or slower speed if chatter develops. Note that chatter is a sign of lack of rigidity. Check again to assure you have done all you can to assure a rigid setup.
#9 Feed. Start with hand feeding, feed slowly but steadily and with enough feed to produce a thin continuous chip (in steel or aluminum). Be aware of tool pressure. The tool should feed in easily if there is enough front clearance. The chip should come off as a curl when everything is right and will roll up on itself. When conditions are right I get a curl that looks much like what the curl of metal that is produced when using a key to open a can of sardines. There is a distinct sound when all is well. To me it sounds like a hissing or tearing sound.
#10 Lubrication. Continuous lubrication should be applied while parting. If you don't have coolant pumped (I don't) use a brush and flood the cut. I find that I can usually work the hairs of an acid brush deeply enough into the kerf to keep things lubed adequately. I use dark cutting oil on steel and stainless and WD 40 on aluminum although the dark oil will work on aluminum as well.
#11 Once you have gotten the hang of feeding by hand and knowing what RPM to use you can mimic the feed rate with your power cross feed.
#12 RIGIDITY! Truthfully that is 70% 0f success so it bears repeating. Do all you can to make everything as rigid as possible. The other 30% is tool alignment and front clearance.