From a personal perspective, I have found that the easiest fasts I have had, came when Yom Kippur was on a Monday, and Sunday morning I did a 3-4 hour run (training for a fall marathon).
My theory is that knowing how dumb an idea it is to do a 3-4 hour run, mere hours before a 25 hour fast, I try to compensate by drinking the rest of the day, every 10-20 minutes having a mouthful or two of water at time.
This is actually how I try to optimize hydration during long distance races, but doing it before Yom Kippur seems to have helped.
Based on a comment from Monica Cellio I feel I should add that the reasoning behind hydrating in the described fashion is based on the uptake rate of the typical persons gastrointestinal tract is about 800 mL to 1 litre an hour. So drinking more than that at once means your kidneys will just discard it.
For your stomach to effectively absorb water you want to keep it constantly absorbing, with a small amount of physical pressure. A couple of mouthfuls at a time keeps the stomach somewhat occupied, and the physical presence helps generate a very small amount of pressure that helps the absorption process.
Thus doing this every 10 minutes or so keeps the pressure up, and maximizes the time your body has to absorb the water.
Of course expect to visit the potty a lot as a consequence of this!