I don't know the reasoning behind no-water urine fasts -- I'm sure there are valid reasons -- but until you know of them and understand them and decide that it's "right" for you, then I would strongly suggest drinking adequate amounts of water during your fast. Don't just jump into urine-only with no water if you don't understand the reasons for it -- it might be something only recommended or helpful in certain situations.
However, I'm sure you can get away with drinking *LESS* water than you would have to if you weren't taking urine, because you're recycling a decent amount of it. But I think it's important to also introduce fresh water into the body intermittently throughout the day unless you have some illness or something where it's adviced to go on urine alone.
Like Foghat said, I think it's best to take the urine un-diluted and give it time to get into your system, but aside from that, make sure you're getting enough water ... if you're getting dehydrated then that's probably a good sign that urine alone is not a viable option for staying at "optimum" levels of hydration ... or at least not with your current body and health circumstances, whatever they may be.