You must change the water in a one gallon container 100% every other day
. When changing the water in the tank, clean the tank and everything in it by rinsing it thoroughly in hot water. This will remove any ammonia residue, feces, and uneaten food that is contributing to the poor water quality in the tank.
I highly recommend getting a tank that is at least two gallons in size. Bettas are tropical fish, and do not thrive at room temperature. They need consistent temperatures in the range of 78-83 degrees to be comfortable, healthy, and active. Most quality heaters are designed for two gallon containers, this is why two gallons is seen as the minimum size for keeping a betta permanently. This is the kind of heater you want: http://www.fosterandsmithaquatics.co...8&pcatid=11368
it has a thermostat and an adjustable temperature dial--this gives you more control and means that the heater will turn on and off as necessary to keep the temperature stable. Surprisingly, not all heaters do this, so make sure you know what you're buying.
Since the fish seems like he's been exposed to a lot of ammonia lately--resulting in his poor fin condition, you should consider getting some methylene blue, if possible. It will prevent secondary infections and will help the fish recover from ammonia poisoning. Try to get a product like this one: http://www.fosterandsmithaquatics.co...fm?pcatid=4822
that is just methylene blue without any other ingredients.