This is always a hard decision and it's really up to you, but if the fish can't swim, the healing of fins does take some time. These are the methods most commonly used for humane euthanasia of small tropical fish ie bettas listed in order of preference.
1. Clove oil. Sold over the counter as a toothache remedy. Place some tank water in a small container with a lid. Add 20-30 drops of clove oil. Lid the container. Shake it thoroughly and let it sit for two minutes. Put the betta in the smallest bowl it will be comfortable in, in tank water. Add the clove oil solution. She will go to sleep and not wake up. Some people add vodka after the fish is unconscious, but this is not necessary. At that sort of dosage she will slip away after a few minutes in clove oil.
2. Decapitation. Put the fish on a hard, flat surface and using a very sharp knife, cut down behind the head in line with the gills. Then pierce the brain with something sharp, like a skewer or the point of the knife. Very, very difficult to do, especially if your fish is thrashing around on the board.
3. Crushing. Read as: two bricks. I wouldn't recommend it for anything larger than a female betta.
4. Ice water. This is not ideal, do it only if you can't get clove oil and can't face the physical methods. Put a cup of tank water in the freezer until a skin of ice forms on the top. Break the skin and drop the fish in. This does take a few seconds, it's not nice. NEVER put the fish in the cup in the freezer.
There are other methods like alka seltzer tablets, but they aren't humane IMO.