It's definitely a bit counterintuitive at first, given that frogs are amphibians, but it's surprising just how many amphibians can survive in primarily terrestrial, or even desert habitats.It's bizarre isn't it, frogs drowning. I found that out in 2000 when we got some tiny frogs from down south. I thought put them in a bucket of water, they all drowned.
We used small plastic containers for water in the frog tanks. If they wanted water they could sit in it and get out easily and there was no chance of them drowning.
The largest body of water a dart frog will probably ever see in the wild are the pools of water that collect in bromeliads, or perhaps a small puddle if they happen to be on the forest floor.
The plastic containers (or water bowls made specifically for herps) are definitely useful, although you have to scrub them out daily with hot water because they often get used as toilets. I figure that a larger water feature with circulation via a pump and some filtration with sponges will help a lot on that front.