A balloon molly showing typical finrot in the tail.
Finrot is a common disease that plagues fish of newer fish keepers for a number of reasons. Finrot is almost always a sign of not enough filtration, as water quality is a major factor in developing finrot. Damage to the fins from bullying or improper decor can open the door to an infection of finrot. Low quality food will not give enough vitamin C to prevent infections. The best way to prevent finrot is by having plenty of filtration capacity (a UV sterilizer never hurts), having proper decor in a tank, stocking fish appropriately, and preventing Vitamin C Deficiency. Even though finrot will damage the fins of the fish, there is no need to worry, as fins will grow back, provided the infection is cleared up first. This is true for any number of problems with the fins.
Finrot will generally be asymptomatic for the first little while, since it is a bacterial infection. Typically, the first noticeable symptoms are going to be tattered or damaged fins with white splotches at the tips. These splotches will grow more opaque as the disease progresses. These splotches can turn gray or black, which can make them hard to spot. If left untreated, the infection will eat away the whole of the fin and spread into surrounding tissues.
Most cases of finrot will clear up once stressors are dealt with. Adding more filtration, doing a larger water change, removing bullies, etc. are all great way to help the fish recover. Adding a little salt to freshwater in addition to other things can be beneficial. If the infection persists, finrot is easily treatable with antibiotics. It is caused by a couple of different bacteria, all of which happen to be gram negative. It can be contagious, as tankmates of infected fish are going to be in the same waters, usually affected by the same stressors. Antibiotics are best given to the fish internally to protect against the infection reaching other internal tissues. Fins are a living part of the body, so internal antibiotics will affect the finrot. If fish won't eat medicated foods, dosing the water can be effective in this case.