Depends on how big your tank is and if you have a filter and live plants or not. If its a fish bowl with no filter and no plants, you should do a 30-50% change every other day at least. If you have a filter with live plants, I do 15-20% once or twice a week in my filtered 3 gallon that has a lot of live plants. If it is in a large tank, like 10 gal, by itself with live plants, you can probably get away with one or two 25% water changes a month.
Think of it this way. The fish is living in the same water where it potties, breathing it in, sucking it in its mouth to eat, etc. Clean water is the first step to a healthy and happy betta. Just put yourself in his shoes and give him a happy, healthy, clean environment. If you wouldnt want to stick your hand in that water, then its too dirty for a fish to live in.