You should probably be doing 50% water changes every day.
You also need to get a water testing kit if you don't have one. Most around here will recommend the API Master Test Kit for Freshwater. You can learn about the nitrogen cycle here:
http://www.fishlore.com/Articles/TheNitrogenCycle.htm
You do not have to let the water set out over night, but you do need to use a water conditioner such as Prime to remove chlorine/cloromine and any other heavy metals that are in your water.
You could use a gravel vac to siphon out about 50% of your water into a bucket. Or you could scoop it out with a cup. You can then dump that water and put an equal amount of tap water into the bucket. Use a thermometer and make sure the tap water is the same temperature as the tank water. (About 80 degrees for a Betta). Add the water conditioner, then siphon or use a cup to add the water back to the tank.
One additional thing, if using a gravel vac, while cycling, go easy on actually vacuuming the gravel since much of the beneficial bacteria lives in that gravel.
Good luck
P.S. Do not overfeed!