I keep an eye on my skin for signs of dryness, or not recovering quickly from pinching, things like that. I think it's just as important though, as with fasting in general, to be prepared to break your dry fast properly.
The most important sign of needing water is natural thirst. Just like the most important sign of needing food is natural hunger. And just the same as your body and/or mind can trick you into eating when it's not necessary, the same thing can happen with thirst. Having a parched throat for example isn't always a sign of needing water. I used to try and quench my thirst with literally litres of soft drink and of course that never worked, and really it was more to make my throat feel better just having the bubbly water go along it and try to scrape away the mucus stuck there which was really what was giving me that parched feeling. The same thing can happen during a fast, mucus lining the throat and giving the impression of a dry throat in need of water. Water doesn't quench this type of thirst because thirst isn't the cause of it.
But of course especially at the beginning we have to be careful and even if we just think we need water it's best to have some water and make sure. So the best way to do this is to take your water in sips. Take one or two sips of water at a time, swirl them in your mouth and swallow as slowly as possible. If you are really thirsty this will at least temporarily feel good, like it is reviving you and rehydrating at least your mouth and throat. Wait ten minutes and see if you still feel thirsty, and if you do repeat the sip(s) and then wait again until the thirst goes away. If you take a sip and you don't feel like it helped at all, or even if it felt good but there was no need for more, then it's something other than thirst going on there.
The rule of thumb is just to drink when you are thirsty, your body knows when it needs water be sure of that, the same as it knows when it needs food. And never go out without a water bottle regardless of how you feel or if you intend to use it. :)
Oh and I should remind you before the moderators step in that posts on 'off topic' subjects like this should be marked O/T in the subject line so that those who only want to read about Water Fasting
don't need to waste time on these little divergences. :)
Take care and good luck with your fasting!