[Damon]

Well welcome to the aquarium world, again.
I should start by asking a few questions.
Are you using tap water for your water source? If so are you treating the water?
There are many chemical in our water to make it safe for us to drink, along with heavy metals. These chemicals are toxic to fish especially delicate ones like neons. You need a dechlorinator at the very least. This will neutralize chlorine and chloramines from your water. There are various ones out there. I suggest getting one that adds electrolytes also.

Is there a heater in your bowl? Neons are tropical fish and thus need a steady temp of around 79 degrees. This is very important also as lower temps will stress the fish out and make them succeptable to disease.

Neons are also a schooling fish and need to be in groups of 5 or more. Any less and they are stressed. There is safety in numbers...........
Did you cycle the bowl? Fish excrete Nh4 which is a form of ammonia. This is toxic to fish. Bacteria grow to break this down into NO2 (nitrite). This is also toxic to fish. Again more bacteria grow to convert this into NO3 (nitrate). This is generally harmless to fish as long as it doesn't reach high levels (above 40). There are test kits you can buy to test for all these as well as test for PH GH and KH. Many say that a 2 gallon can't be cycled. I'm not sure. Water changes should be done at least weekly in a bowl that size. Neons really are suitable for that bowl either. If there is no filter, you will have a hard time keeping them alive in there.

A google search on cycling a tank and test kits is a good start. I hope everything works out for you. Feel free to ask many more questions. We're glad to help.