Here is an excellent link with diagrams:
http://www.bbc.co.uk/gardening/basics/techniques/propagation_rootcutting.shtml

Here's a good method for large roots and large plants:
http://www.hgtv.com/hgtv/gl_plants_perennials/article/0,1785,HGTV_3610_1371784,00.html

This quote may answer your variegation question:
"I have recently read of some interesting results from root cuttings in roses. It seems that there is a higher incidence of sports occurring in root cutting propagation. I am no authority on this topic, but it seems to be due to the fact that while vegetative buds consist of three distinctly separate meristem cell layers in the growing point, root cuttings need to reestablish the three layers from cells that trace back to only one of those three original layers. While the cells should contain the same chromosomes and genetic information, the different layers sometimes harbor mutations and can express different characteristics. This seems to be a unique and exciting way to create new cultivars from old." Randy Hughes and David Zlesa
http://www.ars.org/About_Roses/propagating-root-cuttings.htm

GGG

An easy way to root plants is to cut soft new green growth (bendable) around this time of year. I root camellias, roses and azaleas very easily and pretty successfully this way. Four to six inches of green flexible growth with several leaves on them is good. Strip all but the top two or four years. Stick the piece in water then in rooting hormone but don't get it on the leaves. Make sure the bottom of the piece is also green and flexible. Have moistened clean good quality potting soil in a pot. Stick a pencil in the potting soil to make a hole. Stick the cutting in and push the potting soil around the cutting to get rid of air. You can put several of the same plant in each pot, because some will not take. Keep the potting soil moist but not soggy. I place the pots in a pan with a half an inch of water and refill when empty. Place in a bright shady outdoor location, not full sun or full shade. Some should root in a few weeks to a few months.

Thanks to both of you for the advice. Unfortunately, the shrub I want to replicate has very low success with stem cuttings. Root cuttings were recommended as a more successful alternative, but of course there were no instructions for how to take those cuttings.

Interesting explanation about variegation, GGG. Thanks.