As Mr. Sharret stated,use a sharp positive rake tool. Run your barrel between centers. Don't use a chuck as no matter how you do it you will be stressing the barrel. Besides you'll gain a few inches between centers. With the barrel between centers go 8" or 10" up from your tail stock and cut a place for your steady rest to ride.On a sporter barrel you can use what we use to call a "weatherby contour",similar to what remington uses. On your first and longest taper determine the muzzle dia. and the point your taper ends. Subtract those two measurements an divide the length of the taper in to that an then multiply times 12. The answer will give you taper per foot marked in 1/16" increments on your taper attachment. Do the same for your shorter taper on the chamber end. Run your lathe in high back gear. Take .025-.030 on a side and completely finish your first section. When you get your taper attachment set up don't forget to tighten things up so you are cutting a taper! Your cross feed is locked up so you will be feeding off the compound. When you get to the end of your cut (this is important) get the cutting tool out of your work BEFORE disengaging your feed other wise it will plunge in and leave a deep spot that you especially do not want on your last cut. Once you have figured out your taper your only concern is the muzzle diameter. The rest is blended in. I forgot to mention to run around a .007 feed. As I said earlier you can do 8" or 10" at a time by repositioning the steady rest AND your cutting tool. I sometimes wrap a rag around the barrel to help eliminate chatter. Another important thing to remember is to readjust your tail stock between cuts. Also one of the advantages of turning between centers is that you can take the barrel out of the lathe,put it under some running water to cool it down. I have never had a problem with any warpage. I can turn one in a couple hours. My shop is a throwback to the dark ages so I'm sure there are better ways today but for me this is as good as it will ever get!
PS- Don't set up your steadyrest too tight,treat it like your live center. Also when you start your cut engage your feed before you run your tool in. The opposite of ending your cut. Blend things in with a lathe file and a belt sander or whatever you have. THERE! I think thats it!
