Planting grass under an American Gum tree (Liquidambar styraciflua)
While you may want to have a 3 inch deep layer of mulch around the base of the tree (but kept about 3 inches from the trunk!), it seems to me that you are asking about generally restablishing a nice lawn grass area. Here is a link to an excellent fact sheet from Penn State which will provide the advice you requested, including appropriate grasses, watering requirements, and planting time. Good luck.