You can do 1 of 2 things. You can do a salt dip or salt bath (or you can do both).
A salt dip is 4 Tablespoon (1 Tbsp per gallon for a live in bath) of aquarium salt per 1 gallon. This is done for up to 10 minutes at a time. Start off slow and watch for any signs that the betta is passing out (if they are passing out they will tilt to one side). If they start to pass out immediantly remove and place is regular tank water. This will revive them almost immediantly. You may want to start out doing it in 2-4 minute incriments and gradually increase the amount of time the fish is left in the dip. NEVER leave the fish unattended during a dip!!! You can do up to 3 dips per day, if the fin rot is excessive..for light fin rot..once a day is generally enough.
A salt bath is 1 Tablespoon per gallons. This is a live-in treatment that can continue up to 2 weeks. The longer you choose to use this treatment though..you must gradually reduce the amount of salt over a weeks time period to get back down to regular water after the treament. You don't want to use this for 2 weeks them dump them back in regular tank water. It may (or may not depending on the betta itself) shock their system. You want to make sure you change the water very often and replace with the same amount of salt each time.
You can use either method or both. Using both will clear up your fin rot quicker, although some people are afraid or hesitant to use a dip..it actually works VERY well in treating fin rot. Not to mention helps you not use medications to treat an illness that unless is rampant...does not require medications.
Your fish is in the early stages of fin rot..so I would not use medications at this point. This is also an acceptable to treat a divided tank..as salt will not hurt the other fish what-so-ever.
(always dissolve your aquarium salt in a small cup then add to your tank water and mix up...before adding in your betta. You also still need to addwater conditioner.)
