Woo Hoo!! I can still remember my first batches of dart frog eggs, and how exciting they were! Dart frogs are pretty easy frogs to breed, and the eggs are pretty tolerant of "mishandling", but they can also have a high rate of failure regardless of how you take care of them. In the following few paragraphs, I will go over some of the techniques for dealing with eggs, and how to prepare your tank for the frogs to successfully lay their eggs.
First, the frogs like a secluded spot to lay their eggs, and the choice of most hobbyists is some kind of hut, often a plastic flower pot, with a door cut in the side, and turned upside down. A more esthetically pleasing look is a half coconut shell, with a door cut in the side. A small plastic margarine tub lid, a petri dish, or similar plastic lid is placed under the hut, and the hut it self is placed in an out of the way spot in the tank. Do not put water in the lid, as the frogs will supply a little water to moisturize the eggs, and if you have water in the lid, it will sometimes ruin the eggs. (Likewise, some frogs will lay the eggs in their water bowl. The first time you see this, it is my suggestion to remove the water bowl, or at least empty it, for if they lay in the water, even a shallow layer of water, the eggs will usually be bad.) I use plastic petri dishes, but if you are just going to be dealing with a few clutches of eggs at a time, you can easily get by with something like the plastic tub lids.
If the frogs are laying the eggs in the provided hut, then life is simple! You just need to remove the lid, or whatever they laid their eggs on, preferably about twenty four hours after they have laid them, (to allow them time to fertilize them) and place the eggs in a container with super high humidity. An example would be to put the eggs in a plastic container like a plastic shoe box, with some water in it. Put a layer of gravel or some of the plastic eggcrate material (for lighting, found in the electrical section of the hardware store) on the bottom so the water isnt just sloshing around in the bottom, and place your clutch of eggs on this. Before you place the clutch in the humid spot for incubation, clean any debris away from the clutch, and remove any obviously bad eggs with a pair of tweezers, or the corner of a piece of paper towel. Add a small amount of de-chlorinated water, just enough to wet the bottom of the lid or dish the eggs are in. Keep the eggs at around 75 degrees, and you will either begin to see development within a few days, or the eggs will go bad. Many dart frogs do not start out laying good eggs, but may do so after a season or so of bad eggs, but some lay good eggs right from the start.
While the eggs are developing, remove any obviously bad eggs, and keep the clutch damp. After between fourteen and twenty days, the fully developed tadpoles should erupt from the eggs. I assist tadpoles which have erupted, but are having problems getting out of the gel around them, but don't generally break them out of their egg.
At this point set the tadpoles up in a cup with a shallow layer of water in the bottom. The water should be de-chlorinated, or you might consider using spring water, I find the newly setup tadpole to be the most delicate stage of the whole process. Make sure the water is near the same temperature as the tadpole has been, so it doesn't shock the tadpole. If the tadpole seems active you can put a very small amount of good quality flake fish food on the surface of the water, a couple of specks the size of a pepper corn would be about right. You can also wait two or three days before feeding the tad the first time, they do not do much the first few days. As the tadpole begins feeding, water changes every two to five days are required to keep water quality high. You may need to keep a lid on the cup to keep water temps high enough, since evaporative cooling can bring the temperature of water down as much as five degrees. Check the actual water temperature, and keep it in the seventies most if not all the time. The tadpole should emerge at around sixty to eighty days, depending on species, and conditions. When the front legs pop out of their skin, you will want to lower the water level to a quarter inch or so, and stop feeding them. In a few more days you can set up your new frog in a container similar to those I recommend in my froglet care sheet. The new froglets will take their first food within a few days.