I posted a pictorial on a particular burl last year on Woodnet. Just a few days ago I posted pics of a huge cherry burl, or what I thought was a burl, on a couple of other forums, and one respondent asked if I would post about how I cut it up. I am in the process of that right now, and in fact am trying to make it a general article for my own website. I've since turned a piece, and while I am still not sure it is burl, I am sure it is some of the most highly figured cherry I have ever seen.
But while it might seem complicated, the process is not always. For most burls, I like to let them set while I study them. I look for inclusions and other divisions on the surface that give natural boundaries for cutting a blank. Once the blank is sawn out, then I think about the best piece to make from it. Small bark inclusions can be ignored, but larger ones need to be taken into account for planning the overall shape and orientation of the piece. Large inclusions can make for a very pretty piece, but if they run through the base, you are pretty much done for. Placement of large inclusions also affect the overall appearance and balance of the piece, both visually and aesthetically.
After looking over the "flaws", then shape comes into play. Is it going to be a bowl or a hollow form? Will it be short and fat, tall and thin, natural edged or finished rim? Do I want to emphasize the eyes or the rays? Eyes and rays are the same figure viewed in two different orientations. These considerations will affect how it goes on the lathe for initial shaping. Sometimes it can start on a faceplate, but most often I will start a burl between centers. This offers a huge advantage in that the piece can be reoriented as it is turned if certain characteristics need to be addressed. Voids and inclusions are the chief culprits in causing a shift in the piece, and you will never know until you get into it.
After all that, I sand as much of it on the lathe as I can like I would a regular bowl or hollow form. Often burled pieces require some off the lathe work in the sanding dept. I will oil them or varnish them, although I am starting to think about trying spraying some lacquer. Buffing a burl on a wheel is almost never a good idea, unless you like picking millions of bits of lint out of your piece after the buffing is done. I usually end up waxing them by hand with Butchers, Mylands, or whatever I have in the can at the time, and then blowing out any wax accumulation in the voids with compressed air.
I hope this helps, and when I get my pictorial done, I will at least post a link here, as long as that is okay with the moderators.
Bill