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In caring for an 'ordinary' sick people – those sick enough that they need to lie down, but whose lives are not in danger – rabbinic prohibitions may be disregarded. Biblical ones remain in force.
The easiest and most accepted way of taking care of someone sick is with the help of a non-Jew. For example, it is permitted to ask a non-Jew to turn a light on or off for patients, to turn a heater on for them, to travel to bring them medication, to press elevator buttons for them, and to X-ray them. It is also permissible to ask a non-Jew to drive them to the doctor, as long as the sick person will not do any melakha.
If a non-Jew is not available, then out of necessity, a Jew is permitted to do rabbinically prohibited melakhot the sick person needs. However, the Jew should do them with a shinui. For example, if the sick person needs the lights, heat, or air conditioning turned on or off, the Jew helping should use his elbow or foot, so the prohibition is only rabbinic (27:5 above).
Those who are mildly ill or experiencing minimal localized pain, but can still function normally, are subject to all the Shabbat prohibitions, including the rabbinic ones, just like someone healthy. Nevertheless, they are permitted to take factory-produced medication (i.e., not medication they need to make up themselves).
