Start by cutting back the tops of the plants you want to divide by one half to two thirds. This compensates for the root mass that is inevitably lost. Then lift out as much as the plant's root mass as possible and you're ready to divide. For a large root mass typical of hostas, I go at it with a sharp shovel or even an ax. Don't worry about destroying the plant.
Plants seem to be very forgiving.
Just make sure there a bit of top growth with each root section. Of course, the sooner the divisions get into the ground the better. If it's not possible to accomplish this right away, hold them over for awhile by keeping their roots wet and the plants out of direct sun. Cuttings work best for woody stemmed or creeping perennials. Snip off 4- to five inch shoots.