Finrot is caused by bacteria. When either Columnaris or Aeromonas bacteria infect a fish it could show rotted fins, white fungusy looking stuff around it's mouth or in patches on it's body. It might also have rapid breathing and generally look sick.
These bacteria are always in the tank, but only take hold when a fish has become weakened through any of a variety of conditions that stress it. Some of these are overcrowding, high nitrites, low oxygen content in the water, infrequent water changes, a sudden increase in temperature, uneaten food in the water, being the victim of other aggressive fish. A healthy, well fed fish, living in clean water at a constant temperature will seldom contract it.
To cure bacterial infections, you have to eliminate the cause of the problem and medicate the fish.
I suggest doing a good water change and bottom cleaning before doing anything else. Then treat with an antibiotic such as Kanamycin. This is sold as Kanacyn by Aquatronics or KanaPlex by Seachem. This will treat both Columnaris and Aeromonas infections, which is a good idea because you cannot tell which has caused the infection, and because it is often both. Kanamycin should not effect your biological
If you are unable to get Kanacyn, Maracyn AND Maracyn2, used together, will do the same thing. Tetracycline will also work, but is much more expensive.
While the fish is being treated, it is helpful to add an airstone to the tank to increase the oxygen content of the water and lower the temperature to no more that 74-75 degrees. These things will slow the ability of the bacteria to reproduce which will promote healing.
When the fish is healed, take care to feed it well and keep the water conditions as perfect as possible to avoid reinfection. Remember a recently ill fish is still weak and likely to become infected all over again if conditions permit.