There are individuals who, due to specific health issues, may need to eat or drink on Yom Kippur. A person who is in an immediate situation of pikuach nefesh must eat or drink as much as he needs. However, often, a person is not currently in a life-threatening condition, i.e., pikuach nefesh, but must eat or drink to avoid reaching a life-threatening situation. In this case, who much may this person eat?
We must first determine the shiur of karet, i.e., the quantity of food which one must eat to become culpable (karet) on Yom Kippur. The Talmud (Yoma 73b) teaches that only one who eats the volumetric equivalent of a large date (kakotevet hagasa) is culpable on Yom Kippur. As it is difficult to determine this measurement, the rabbis say this is approximatly 2/3 of an egg (kebeisa). As a kebeisa is approximately 56 grams, the poskim say that a kakotevet hagasa is about 36 grams. Also, this amount must be eaten within a certain amount of time, called k’dei achilat peras, the amount of time it takes to eat half of a loaf of bread, which we assume is about 5-10 minutes. If a person ate a shiur of kakotevet hagasa within that amount of time, he is culpable on Yom Kippur.
It is preferable, when possible, for a person who must eat on Yom Kippur to avoid a hiyuv karet. Therefore, we generally instruct a person to eat about 30 grams, and to wait ten minutes, and then to eat another 30 grams, and then wait, and then eat another thirty grams, etc. This behavior is known as eating b’shiurim.
In this case, should he should say the hamosi blessing before eating. Furthermore, if he eats a kezayit, which is a bit less than 30 grams, then he should say birkat hamazon. What about netilat yadayim? If a person eats only 30 grams, then he washes his hands, i.e., netilat yadayim, without a blessing. If he eats the quantity of two olives, e.g, if he ate another thirty grams ten minutes later, then he should say the al netilat yadayim blessing. Hacham Ovadia Yosef rules that one who washes netilat yadayim on Yom Kippur may wash up to his wrists, as this washing is not for pleasure (letaanug).
Summary: One who receives permission to eat on Yom Kippur should preferably eat b’shiurim, i.e., about 30 grams in ten-minute intervals. If he eats bread, he must say hamosi before eating, and birkat hamazon, if he ate a kezait, afterward. Regarding netilyat yadayim, he should only say the al netilat blessing if he plans to eat more than two k’zeitim; in this case, if he eats 30 grams of bread at least twice, he should wash with a blessing.