Hello and welcome to the forum.

Distilled water is never something you need to use, but many use this for misting, since it leaves no mineral deposits/residue on the glass, which just makes it looks nicer. If this is nothing you care about (or don't mind cleaning it), tap water is fine for misting.
As the water source, you do not want to use distilled water. The frog needs certain things from the water, and distilled contains none of these things. In addition to this, distilled water actually removes some of the good things in the frog (being completely empty, you could say it absorbs stuff to saturate itself (this is not accurate, but it's an easy way to describe it, since I'm not that good at the actual chemistry myself). You want to use conditioned tap water as the water source. There are tons of different brands out there, most for fish (but they work equally well). I personally use Zoo med's ReptiSafe and I think it's good.

Some use bottled spring water instead of conditioned tap water and supposedly this works. However, I personally feel that it's safer to go for the conditioner, since you can't always be certain if the spring water is safe. According to one the very knowledgeable and experienced frog keepers here (sadly, I don't remember who it was...), conditioned tap water is actually better than spring water.

Lastly, here's some nice reading for you: http://www.frogforum.net/vivarium-te...hing-else.html