Private hospitals are quite luxurious in Mexico. The quality of care is world class. It is important to understand that care will cost less than back home (if you were paying directly), but that there are still significant amounts involved, for example, in a surgery and one-week hospital stay.
It is expected that the patient will be cared for during a hospital stay by friends or relatives. This applies especially in the public system, but also in the private hospitals. There is usually a pharmacy attached to each hospital, so prescriptions are not difficult to obtain, but still must be paid for. If the patient is not mobile, they will require assistance throughout their stay.
There is no universal blood donor system in Mexico, and consequently there is no central blood bank. Each hospital or clinic is responsible for its own supply. If a patient requires a transfusion, the hospital will expect the friends and relatives of the patient to mobilize and donate at least an equivalent amount.
There are a variety of ambulance services available throughout the country. None are public in the sense that they are funded by tax money. The Red Cross operates one of the most comprehensive services, and in the case of traffic accidents, for example, will be the agency called by the traffic police to assist injured victims. Other, higher end services can be subscribed on a monthly premium basis similar to an insurance policy.