IF your betta does not get better after you have tried the various treatments listed here, and IF you decide that euthanasia is the only solution to end the suffering of your fish, definitely look for methods that are quick, humane, and relatively painless.
clove oil is used for dental pain by many people. it is an anesthetic, and like all of the chemicals in that category, will cause death with an overdose. only buy a high-quality oil, but realize that it will cost several dollars.
freezing - seems humane, but only if done properly. putting the fish into some water and then into the freezer takes a long time. ever wait for water to freeze so you can have ice cubes? it takes longer than that. sometimes enough time for the fish to decide they want to live and jump out of the container, only to die out of the water, frozen to a box of bagel bites. a better and faster way of freezing is to put your container of water into the freezer long enough to form a thin layer of ice on top. break the ice, and drop your fish into the cold water. no waiting - the body temperature immediately drops down and the fish becomes unconcious right away, then dies. this doesn't work for larger fish as they hold more heat internally and would take too long.