If you don't have live plants, you can treat him in-tank with aquarium salt. If the tank is less than 5g, change 50-100% of the water daily. Over 5g, change 25-50%. If you have live plants or you just want to make water changes convenient, treat him in a small QT container and change 100% of the water daily. Dosage is 1 tsp of aquarium salt per gallon. Let the salt dissolve first in a little bit of tank water. Continue the salt treatment for maybe a week, no more than 10 days.
No, the salt won't kill him. Some betta breeders keep a small bit of salt in their tanks at all times as a preventative measure. If you don't feel comfortable with the amount, you can always put in maybe 7-8 tsps instead of a full 10. Alternatively, if you really don't feel comfortable with the salt at all, you can try tannins. You get these from Indian Almond Leaf, which can be veerrrry hard to find or clean and naturally dried oak leaves crumbled into the tank. You can also use a decaffeinated green tea bag (no flavors added, so no lemon flavoring or anything, just straight green tea) or a rooibos tea bag.
So in 10 days I should change the water? I usually just do 100% water changes when I do clean the tank, so I'll just do a 100, or will that shock him because he's coming from a salty tank and going into a clear tank?
During the ten days of his treatment you'll want to change maybe 25% of his water every other day and redo some of salt treatment. So if you take out 2.5 gallons during the water change, put in 2 tsp of salt. If you don't want to shock your guy, you can do this:
on the 8th day of treatment, change 25% of the water but replace it with water that has NOT been treated with salt. There will be 25% less salt in his tank.
on the 9th day, change 50% of the water and replace it with clean water, no salt. 50% salt in his tank.
on the 10th day, change 100% of the water. By then, the change from salt to non-salt should have been gradual enough that he won't be too shocked by the change.