One who received permission to eat on Yom Kippur, based upon the recommendation of a doctor, should not eat regularly, instead, he should eat b’shiurim. Therefore, this person should eat less than the shiur of kakotevet hagasa (a large date), the amount for which one is culpable on Yom Kippur, in intervals of more than k’dei achilat peras, or approximately every ten minutes.
At times, a doctor may instruct a person to drink on Yom Kippur, to be adequately hydrated. How and how much should this person drink on Yom Kippur? The Talmud (Yoma 73b) teaches that one who drink melo lugmav, i.e., a cheek-full of liquid, is culpable on Yom Kippur. Although this amount is relative to the size of a person, it is assumed to be about one and a half ounces. Therefore, we instruct such a person to sip water, without drinking more than a cheek-full (about an ounce), preferably, in the same time-frame mentioned above. i.e., every ten minutes. This is the view of Rav Ovadia Yosef.
Interestingly the Shulhan Aruch was more lenient. He rules that the shiur of Yom Kippur is the amount of time it takes to drink a re’vi’it of liquid. According to this opinion, one can drink a bit more than an ounce of water after ten seconds or so. This view should only be relied upon if a doctor insists that the holeh must drink this much liquid.
Finally, if a person receives permission to drink on Yom Kippur, is it preferable to receive liquids intravenously? R. Ovadia Yosef (Yalkut Yosef, Hilchot Yamim Noarim, pg. 371) cites R. Shlomo Zalman Auerbach who ruled that we do not recommend receiving liquids intravenously. He expressed concern that people may mistakenly believe that a person should be strict, and not drink on Yom Kippur, which may one day endanger the life of a different sick person.
Summary: One who must drink on Yom Kippur is instructed, to drink, if possible, about an ounce of water every ten minutes. We do not tell the sick to receive liquids intravenously on Yom Kippur.