The #1 cause of death of a new betta is ammonia poisoning. If the tank is new, its going to go through the cycling process which normally takes about 1 month to complete. During that time you'll get ammonia spikes which can burn the bettas gills, and lead to all sorts of complications. If you're already made it past that point, congratulations. Should be easy from here on out.
I highly suggest getting a Marina C10 heater (available at Petsmart). Unlike other "betta heaters" this one has a thermostat in it to make sure the water stays at 78F, which is the idea temperature for a betta.
Adding some java fern, anubias, or java moss to the tank will help keep the water oxygenated between changes, as well as help absorb ammonia caused by fish waste or uneaten food. They all do well in low light and don't need fertilizers added to the water.
Finally, when changing water, make sure to treat it with dechlorinator before adding it to the tank, and try to make sure the water going into the tank is the same temperature as the water coming out.