Maintaining lush, healthy turfgrass under shaded conditions can be a significant challenge. The most important management consideration is selecting the most shade tolerant turfgrass.
For warm season turfgrasses, in order of most to least shade tolerance, St. Augustine grass, centipede grass, and zoysia grass are good choices. For cool season grasses, fine fescue and shade tolerant varieties of Kentucky bluegrass work well. Roughstalk bluegrass, often referred to as Poa trivialis also does well in the shade.
From a management point of view, the amount of nitrogen fertilizer applied should be about half of that used for the same species growing in full sun. Mowing height should be raised to the upper portion of the recommended range. Watering should be infrequent, but deep, making certain to thoroughly irrigate the entire root zone of the turfgrass.
Of course, all essential nutrients (phosphorus, potassium, etc.) should be maintained at recommended levels. A soil test should be conducted to ensure that sufficient levels of these nutrients are present.
It's also helpful to minimize traffic over the area.
Finally, pruning low hanging branches and even some selective pruning of limbs in the tree canopy will allow more light to filter through to the turf surface.
In some cases, there simply is too much shade for any turfgrass to survive, and a ground cover such as ground ivy or pachysandra should be used.