1.) How big should the tank be for just that one frog, like the smallest it can be.
I would not keep any frog in something smaller than a ten gallon tank. And many frogs will outgrow even this size. There are always firebelly toads, but I guess those are toads and therefore would not fit your idea of getting a frog.
Although, their habits are more froglike than toadlike (they spend alot of time in water, something that most bufo toads do not do.)
If you wanted anything like a treefrog, I would suggest getting a taller tank, like maybe a 45-gallon tall, and creating a terrarium with branches and stuff for the frog to climb on. for something semi-aquatic like a leopard frog, I would suggest at least a 30-g-long tank so they can jump around; but bigger is better.
2.) do I have to have something in the bottom immediately, like moss? Or will it make a big difference in my frogs health?
Some frogs do best in a half-land, half water setup. The water does not have to be that deep, just enough so the frog can submerge if it wants to. Frogs that like these setups include leopard frogs, green frogs, firebelly toads, and bullfrogs (though theyg et way too big for beginners to keep, and need tanks that exceed 125 gallons!)
Treefrogs do not require deep water and could actually drown in it. I have no real experience keeping thoese though so someone else would hafta help you on that one.
Horned frogs are awesome fat frogs, but they spend much of their time burned in the substrate. They only really need a 10-g tank because they are not active at all. That, and a waterdish sunk into their substrate and not too deep (they are not noted for their swimming ability. 
3.)ok, what kind of water dish should i put in the tank, and is the water out of the sink ok if i let it sit 24 hours? I personally use purified water that's free of chlorine. As long as your water is not wellwater with high concentrates of minerals, I would assume it's safe (if you drink it!) But some conditioner that removes chlorine may be on order.
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