Well, first off, and not to be mean, but a half gallon tank really is not big enough for a betta to live in. I would go for at least a 3 gallon tank. Some may argue that even that isn't big enough, but I think its the bare minimum a fish like a betta should be housed in. They also need a source of heat or they will start to shut down aka not take food, stay in one place in the tank, that sort of thing. There should be a tank heater in there because they are tropical fish after all.
Now that we have that out of the way, a healthy betta should be swimming around in their cup/bowl or what ever they are in at the store and engage in flaring. Their fins shouldn't be clamped and they should have bright and alert eyes.
“The day the power of love overrules the love of power, the world will know peace.”
― Mahatma Gandhi