Many types of yucca transplant fairly easily - sometimes if you yank off an
offset (a side clump to the main clump) and stick it on some moist but quick
draining soil, it will root in fairly quickly, especially if you get a few
of its own already developed roots when you yank it up. If you are digging
up a main plant, I would try to moisten the soil and get as much of the root
as possible, as well as the dirt around it - preferably all in one large
shovelful.
Make sure that you put the plant somewhere well-drained - yuccas prefer
drier, sandier, well-drained soil and usually will not make it in moist
clayey soils that stay wet or damp all the time. If you have that kind of
soil, I would probably make a pile of sand, gravel and dirt on top of your
existing soil, making a mound six inches or so higher than the main level of
soil, so that you can put the yucca there where excess water will drain
away.