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Monkey grass is hardy to zone 6. If you live in a zone lower than 6, it will not survive in normal parts of your yard. That being said, if you are in zone 5, you may have or be able to create a microclimate in your yard that can bump a small section of your garden up to a zone 6. This article will explain more about creating micro climates:
https://www.gardeningknowhow.com/garden-how-to/projects/how-to-make-a-microclimate.htm

This article will help you with liriope pruning: https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/pruning-monkey-grass.htm

Monkey grass needs a good bit of light, so if it is a somewhat shady area, it might not do well. Any of the plants in this article would work well: https://www.gardeningknowhow.com/special/shade/ground-covers-for-shade.htm

If it is a large area, some people will set their lawn mower to the highest setting and will use a lawn mower. A weed wacker will work too, but it will look a bit ragged for a bit while it regrows.

Monkey grass typically does not require any fertilizer, and in some cases, can even get out of control. To learn more about this plant, this article should help you:
https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/monkey-grass-a-spectacular-groundcover-for-the-lawn.htm

Monkey grass should not be affected by grass specific herbicides, like Grass B Gon. They are designs to harm lawn and weed grasses rather than ornamental grasses. Just to be safe though, test on a small area before spraying the whole area.