Most people use the average fish food from the store, but yet they don't understand why there fish don't last long. They don't realize that different fish need different food. You can look that up online or just ask the manager of a fish shop. When feeding a fish make sure that you do not touch the fish food. This can be harmful for the fish.
When changing the water the fish should be put in a glass container until the water has been changed or the bowl have been cleaned. To clean the bowl take the fish out like before. Then, dump out the water. Next, you scrub the fish tank. Then, you rinse it out good. Make sure you do not leave any soap in the fish tank.
Betta's, like all fish, do best in the largest, temperature controlled, filtered body of water you can provide. That stated a Betta can live in as little as a gallon of water without a filter or heater. You should clean the bowl as often as possible, no need to use any form of soap, just scrub it well and refill it. Use some form of dechlorination in the water you put back in the bowl (that can be purchased at any pet store). Touching the food is not a no-no but make sure your feeding it the right food. Betta pellets are usually sufficient, flakes are usually not. I feed my Betta freeze dried blood worms with my fingers.
If your fish is a gold fish its probably going to die. Goldfish need large bodies of cool water to live in any sort of real health. A minimum of 10 gallons a goldfish is usually recommended. Goldfish produce large amounts of waste and will end up stunted by these toxins in smaller bodies of water.
Please do further research depending on the type of fish you intend to keep. My favorite place for such research is The Freshwater Aquarium. Its a google mailing list but you should be able to read the discussions without subscribing. If you really like fish keeping by all means subscribe.