I don't cycle mine either. I just don't want to go through all the testing and constant water changes. Every summer for a whole week, I have to test the water in my pool 3 times a day and it's a pain in the butt. It involves a test kit and water samples and writing everything down. Its a big pain but required by the health department.
Allowing a tank to mature ,or cycle, with fish if done properly,,requires no constant testing or frequent water changes. Problem lies with those who start with too many fish, too large of fish, inappropriate fish, and overfeeding of fish.
One betta in a ten gal tank that was filtered ,,and heated ,and water was treated with dechlorinator such as PRIME, would not in my view need frequent water changes assuming,(always a bad thing) that this fish was not being overfed. The biological load on ten gal would be small.Through testing every couple to three days, again,,assuming the fish isn't overfed, water changes may only be needed once or twice a week. Were it my fish,,(and it ain't)I would feed the fish once every two days maybe even three. Sounds cruel to some, but anymore than that and As some have stated ,,Water changes would be more frequent .Only tests can dictate the frequency.
Yes, in the begining of a cycle you have to test the water regularly to monitor the nitrogeneous substance levels in the tank. A full test of ammonia, nitirite, and nitrate takes about eight minutes. And really until you see the nitrites start to dip you don't need to do a nitrate test so it takes only about five minutes. If you see levels higher than 0.25ppm you do a water change. When I cycled my first fish tank I had to do a water change about every three days. I tested daily though just to be sure.
The good news is that once your tank is cycled you only test the water once a week when you do a partial change. In the long run you'll do fewer water changes when you cycle your tank. You'll also have healthier, more active, and longer lived fish.
I already have a betta in the tank. They don't want to pay for the kits and ammonia, etc. They think it's too much money. If I don't cycle the tank, how often do I need to change the 10g water and how much?
If you can get a turkey baster, just for cleaning debris out of the tank and not used for food, you could probably do partial changes once a week and a full change once a month. What I'm doing with my 4 gallon is about every week to 10 days, I take out half the water and replace it with clean, dechlorinated water, the same amount that you take out. Then once a month I dump out all the water and rinse all the rocks and his plant with hot water. You never want to use soap or any kind of cleaning solution because that will kill your betta. Then I fill it up all the way with clean water. In between full changes, I use the turkey baster I got specificly for this purpose, to clean debris off the bottom of the aquarium.