Alongside our house, we have a big section of variegated Liriope (a.k.a., monkey grass or spider grass). Liriope is a great groundcover that requires little in the way of upkeep, though you’ll want to cut it back once a year to keep it looking nice.
The main problem with Liriope is that the old leaves can get a bit tattered during the winter. Fortunately, it’s very easy to prune away the old growth and get your plants cleaned up and ready for spring.
In terms of timing, you don’t have to be particularly careful. Anytime between fall (when your lawn goes dormant) and spring (before the Liriope starts growing) is fine. Just don’t wait too long, or you might clip off the tips of the new growth, leaving you with squared-off, ragged leaves.
As for how to cut it back… Once again, you don’t have to be particularly careful. I usually grab the leaves in a bundle and then use a pair of kitchen shears to cut of the old growth about 2-3 inches above ground level. As my son said “This is kinda like giving it a haircut, except you don’t have to be as careful.”
The preceding picture shows what one of our plants looked like about a week after it started putting on new growth. You can see the old growth that’s been cut back around the edges, as well as a bunch of new leaves coming up in the middle.