Taking care of dart frogs is relatively easy. As long as you take your time and get properly prepared there wont be any issues.

Some good starter species would be D. Leucomelas, D. Azureus (or other Tinctorius morphs), and D. Auratus.
All great species, and favorites in the hobby.

Here a small over view.

Temperatures - 70-80 day times, 65 low and night. For the most part mid 70s is perfect.
Humidity - Around 80% (glass lids should cover at least 90% of the tank)
Housing - They should be housed in a vivarium with live plants. The vivarium should consist of a drainage layer, soil, leaf litter and live plants.
Food - Dart frogs should be kept on a stable of fruitflies. Keep in mind the fruitflies need to be dusted in supervine high quality supplements.
I recommend learning to culture flies before purchasing your frogs.

Just take your time, ask tons of questions, read, and read some more and you will have no issues.
Enjoy!

Feel free to PM me with any questions you have or post here