I would say a 20 gallon long flipped to its side with a protective screen the LEAST amount of space you can give a single one. I'd shoot for something 30-40 gallons so you could house a pair. They are best in a community with same species frogs.
These guys are not for the most beginner of keepers as they can be delicate, they need a wide ranging diet, and their day and night temps are different.
These guys cannot be handled. It's best to leave them in their cage and watch them act in their natural environment. They absorb toxins and water through their skin so anything that you have on your hand (natural oils, bacteria etc) they get.
The tank must have tons of arboreal climbing branches, leaves, bark and whatnot to climb on. They need a high humidity and the day time temps should be around 86 F, during the night it should be 75-78 F.
Another important thing is MOST FROGS will not tolerate dead or freeze dried food. They need living moths, flies, crickets in the cage to eat.
You should mist the cage down with warm water thoroughly every day or get a reptile fogger. The cage should also be clean and healthy for the frog. To raise the humidity shaved coconut substrate like Eco Earth. A small dipping pool, very shallow, should be provided.
You can put a heat mat on the back of the tank to maintain temperatures and have a night bulb, at low wattage, to maintain night temperatures. Make sure you have perfectly fluctuating temps or you will kill the frog.
I would first get some frog experience under your belt before you attempt a Red Eyed Tree Frog. There are fire belly toads and pacman toads that are easier to maintain.