Halakhic literature discusses the requirement to fast on the two 25-hour fasts, and how just about everyone is obligated to participate, even pregnant and nursing women (who are given dispensation on the minor fast days), and how seriously the Jewish community should view these fast days and their personal observance of them.
A healthy person who can manage 25 hours without food or drink should do exactly that - no food or drink for 25 hours.
That being said, exceptions are made for those who cannot fast due to medical reasons. (See Shulchan Arukh 612 + 618)
One approach encourages people to utilize the פחות פחות מכשיעור method, which allows for someone who must be hydrated, for example, to consume around 1.5 oz every 9 minutes. In other words, drink some water (or other hydrating drink) in a small shot glass, then do it again every 9 minutes (that distance of time prevents the two 'shots' from being considered a "combined" consumption), and the person is still considered to be fasting.
People who have more complicated medical situations, in general, should eat what is needed to tide you over until after the fast. Don't have a multi-course fancy meal! But be sure to eat what is needed, perhaps once mid-day, perhaps an early morning breakfast and an early afternoon mini-lunch, and then wait until the day is over to have the traditional "break-the-fast-meal" with other family members or friends.
There is a simple rule: If fasting will wind you up in the hospital, you are WRONG if you insist on fasting.