If the tank is filtered and cycled then I do partial water changes every 1-2 weeks. Vacuum gravel at the same time. Amount of water change varies depending on size of tank, if the betta has any other tank mates and if the last water change was a week ago or two weeks ago. I tend to change between 25%-50%.
If the tank is unfiltered and smaller than 5 gallons then %100 water changes are done every 5-7 days. It really depends on tank size, size of the betta, and how much they are being fed. Smaller tanks will require more frequent water changes. The only way to know for sure is to test for ammonia daily. If ammonia shows up on day 5 then you would want to do water changes every 4 days (again I'm talking about unfiltered tanks/containers)