This is such a broad question that it's difficult to generalize. There are different types of "nursing home" facilities and different levels and types of care provided within those facilities, all of which contribute to a wide variety of "typical day" patterns.
All nursing home facilities are going to provide room and board for residents. This will include help with personal cares, laundry, housekeeping, and activities throughout the day or week to keep the residents physically and mentally active. Residents may have a private room or may share a room; furniture may include personal items or all belong to the facility.
In some places, meal times are set by the facility and all residents eat in the dining room at those times. In other facilities, residents have more control over when they choose to eat, so there may be a range of time when a certain meal is available and residents eat as they wish.
All nursing home facilities will control the administration of medications needed by residents. Most have medical doctors who make periodic visits to assess residents' health and changing needs.
Nursing homes may or may not provide therapies of various sorts for residents who need therapy as they recover from illnesses or surgeries.