first thing, seperate both of them, if one is more injured than the other you might watn to get another 1 or 2G tank for him to recover, so he wouldn't constantly be in the sight of another betta and cuase stress.
Remove the injured one to his own tank. Nwo the most important thing you watn to do is to prevent finrot on him. To do this, keep the water EXTRA clean, whcih means change the water every day or every other day. Add the proper amoutn of salt into his tank, and add some finrot medication if you have any. (such as melafix). Raise the tempreature to 80 if you can, if you dont' have heater in his tank, put him in the warmest room in you rhouse.
If you see that he is stil stressed out, try covering his tank with a cloth, this should calm him down so he wouldnt' have to be alert looking out all day.
Keep up with the medication until you start to see new growth on his fins, which is usually clear and transparent. Depending on the damange made, you should see an uphill or downhill progress in about a week or two.
It woudl be good to supplement his diet with some frozen food if you have any. Feed him regularly, but make sure you take out uneaten food on the bottom of the tank. The key here is to keep the water as clean as you can.
Good luck!
