The next level of betta fish fin rot is:

Fin rot isn’t a disease. It’s a symptom of some other disease or problem with your fish.
Photo provided by Flickr
As with standard water changing and fish transfer, make sure the water of both aquariums are the same temperature before moving your betta. 77 degrees is nominal and can be easily keep at this temperature with an aquarium heater. If the temperature is too much higher, the fin rot bacteria can grow and spread faster. If the temperature is too much lower the betta will be too cold in general.
Although any fish can get fin rot  and  seem to be particularly susceptible.
Photo provided by Flickr
Finrot is probably one of the most preventable and easy to cure goldfish diseases. If left untreated, it can ill the fish and also infect all the goldfish you have in the tank. This is a bacterial infection.The most common cause of Finrot is poor water quality. Tank may also be overcrowded and fish are stressed from noise pollution. Rough handling, fighting or very low water temperature(below 50oF) can cause this disease. I also have a second fish which is a yellow tang (~4") that has developed fin rot. Here is a photo.
Photo provided by FlickrFin and Tail Rot in betta fish.
Photo provided by FlickrFinrot is a common bacterial  of fish kept in low quality water conditions.
Photo provided by Flickr
Fin Rot in and of itself is not contagious, but if you keep fish in a community tank you may end up with several fish contracting the infection. This is because the bacteria that cause Fin Rot are opportunistic bacteria - poor water conditions stress fish out, and when fish become stressed, their immune systems become weak. Weak fish are not able to fight off illnesses that healthy fish easily can. So if you have poor water conditions or something else causing stress in the occupants of your tank, you may have an "outbreak" of Fin Rot.Enough of the "isolate your sick fish" lecture (you're probably sick of it by now if you've been through other parts of this site, right?). Fin Rot is caused by gram-negative rod bacteria. Fin Rot can be easy to treat if you catch it early enough and maintain your water quality pretty well, or it can be a complete pain in the bottom if you don't catch it early enough or allow your water conditions to fluctuate over long periods of time (you know, we all get lazy every once in awhile).Even though Fin Rot is not contagious, it is still a good idea to isolate a betta that you are attempting to treat for Fin Rot. There are several reasons for this, but the main reason is that it's much easier to keep the water absolutely pristine when you have a fish in an isolation container. The secondary big reason (maybe this should be first) is that many medications used to treat fin rot can kill your biological filtration, live plants, and may be harmful to other animals in your tank (depending on the medication and the other animals). It's also just generally a good idea to isolate any sick fish when treating them so that they are not getting picked on and there is no chance of passing any secondary infections on to other fish, as well as making it easier on you to monitor the health and progress of your fish. Severe cases of fin rot (fins just seemingly melting away and falling off in big pieces or when the rot is close to the body) should always be treated with an antibacterial fish medication like Sera Baktopur Direct or Tetracycline. Products like Melafix, Pimafix and Bettafix do not cure fin rot and may actually make it worse.Fish Fin rot is a bacterial disease that commonly affects aquarium fish. Fin rot is also a disease that can easily be prevented by maintaining correct care for the fish and at the same time very easily caused by incorrect care, such as, bad water conditions and injury, one way or the other. Fraying or torn fins, enflamed fin base and, if not treated in time, the fin rotting away are symptoms of this disease. White may appear on the affected parts which is generally bacteria. As the disease advances the fins will get notably shorter, becoming red and enflamed along with bloody patches. To treat a betta with fin rot using aquarium salt, transfer the fish, a heater and some hiding places like real/fake plants to a separate or tub with treated tap water of the same temperature as the water in the aquarium (be sure to give the fish some time to acclimate to the 100% tap water)! Set the heater to a temperature of around 77-78 F – any higher will make the rot progress more quickly, and any lower and it might be harmful to the fish.