If an ill patient’s condition on Yom Kippur is life-threatening, Heaven forbid, then he eats and drinks as usual without any restrictions. The Torah is more concerned about human life than about fasting on Yom Kippur, and thus a dangerously ill patient’s top Halachic priority on Yom Kippur is his health. The Torah instructs, "Va’hai Bahem" – we are to live with the Torah, and not die as a result of Torah observance, and thus a dangerously ill patient eats and drinks on Yom Kippur without any Halachic restrictions whatsoever.
This is not the case when dealing with a patient whose condition is not life-threatening, but who is nevertheless medically required to eat in order to protect his health. An example would be a woman who just delivered a child, or a patient who feels very weak. Although such patients are allowed and required to eat on Yom Kippur to maintain their health, they must ensure not to eat in a manner that would, in the case of a healthy person, render one liable to the punishment of Karet. A person is liable for Karet for eating on Yom Kippur if he eats the quantity of "Kotebet Ha’hagasa" – a large date – within the period of "Kedeh Achilat Parres." The Poskim identify the size of "Kotebet Ha’hagasa" as two-thirds of a "Ke’besa" (volume of an egg), or 36 grams. The period of "Kedeh Achilat Parres" is identified as between five and ten minutes. Accordingly, Hacham Ovadia Yosef ruled that an ill patient whose doctor instructed him to eat on Yom Kippur should eat 30 grams of food, and then wait ten minutes before eating another 30 grams. This way, the patient is able to eat as much as he needs to without transgressing the Karet prohibition according to any opinion. The patient (or those caring for him) should weigh food on a scale before Yom Kippur to determine the amount he is allowed to eat, and if necessary, one may weigh the food even on Yom Kippur.
If the patient eats bread, he of course recites the Beracha of "Ha’mosi" before eating, regardless of the amount of bread he eats. Netilat Yadayim is required if one plans to eat at least 30 grams of bread. If he plans on eating less than 30 grams, he does not need to wash Netilat Yadayim, and if he plans on eating between 30 and 60 grams, then he washes without a Beracha. If he plans on eating 60 grams or more of bread, then he washes with a Beracha. Therefore, in the case described above, where a patient eats 30 grams of bread, waits ten minutes, and then eats another 30 grams, he must wash Netilat Yadayim with a Beracha. Birkat Ha’mazon is required if one ate 30 grams of bread or more.
Hacham Ovadia Yosef ruled that even if one will be eating less than 30 grams of bread, he may wash Netilat Yadayim is he so desires. He adds that one who washes Netilat Yadayim on Yom Kippur washes as usual, up to the wrist. Since this washing is done for the purpose of satisfying a Halachic requirement, and not for enjoyment, it is entirely permissible, and no restrictions apply.
Summary: If a patient whose condition is not life-threatening is medically required to eat on Yom Kippur, he should eat up to 30 grams of food at a time, waiting at least ten minutes in between. A patient whose condition is life-threatening, G-d-forbid, should eat and drink as much as he needs, without any restrictions whatsoever.