I've used normal "corky" handlebar tape, medium weight cotton twine and amber shellac on these handlebars. Wrapping over and pulling under the twine (or other string-type substance) as a finishing is called whipping. The shellac works to glue it together and make it look nice.
Note that this isn't a hard process, but it does take some time - and it can't be undone without destroying the materials used. So make sure your brake levers (if applicable) are where you want them and you've got the right stem on if it's a quill like this one, because you're not going to be able to change them later without undoing this and starting over again!
(final result photo updated 7/5/2007)
Step 1: Things you'll need
Electrical tape for the initial bar wrap.
Cotton twine. I use plain white medium weight cotton/polyester, it's cheap and looks good. I've tried the hemp-type hairy kind but I didn't like the stray fibers or the feel of it after applying the shellac. I like the cotton because it lets the shellac soak in and color it, as well.
Shellac; I use amber because I like the coloring effect, but clear is available too, of course.
Denatured alcohol to thin the shellac.
Rubber bands (to keep the levers from flopping around) or just tie them out of the way with some twine. I find it insanely easier to do this with the handlebar assembly off the bike.