Is the vegetation under your shade tree thin and lifeless? If so, you may wish to consider planting a groundcover instead of turfgrass. Periwinkle, English ivy, lamium, pachysandra, some cultivars of coral bells, ajuga, plumbago, euonymous, Virginia creeper and Hall’s honeysuckle are good options to consider. The bottom line is Right Plant, Right Place, and under shade trees, turfgrass is often not a good choice.
May is a great month to plant groundcovers. First, use a pitchfork to loosen the soil and work in an inch or so of compost. Next, remove the plants from their containers, inspecting the roots as you go. It’s important to untangle any that have encircled the pot. Groundcovers can be planted anywhere between 6 inches and 18 inches apart, depending on how quickly you want them to spread and form a dense mat. After planting, water them thoroughly to settle the soil. Application of a preemergence herbicide such as Preen will help suppress annual weed germination, as will applying 2 inches of wood chips.
Regarding groundcovers, unless it’s a short, closely spaced perennial, it may spread where it is not wanted aka become invasive. When this occurs, it’s important to be ready with a hoe and dandelion digger to keep the spreading to a minimum. When these plants spread into lawns, traditional broadleaf herbicides such as Trimec, Powerzone and Weed B Gone Maxx can be used according to label directions. Regular mowing will also keep some at bay.