Welcome to the forum.
He'll heal his fins by his self so long as they do not become infected.
To keep them from becoming infected and help him heal the fins make sure that he's in warm 78-81 degree water. Keep the water as clean as possible by changing 25% of the water at least once a week if the tank is cycled. If it's not cycled then keep an eye on the ammonia and nitrite levels, change the water 2x a week or when ammonia or nitrite get above .25ppm. You can add Seachem Stress Guard, and Indian Almond Leaf to the tank to further keep infection away both.
To enhance his color your best bet is to keep him in clean, warm, water. Having lots of plants, either fake or artificial silk will help hi feel safe and less stressed which will also cause his colors to come out. You can use plastic plants but make sure too run a pair of panty hose over them before putting them in the tank, if the panty hose snags then your betta's fins can and you shouldn't use the plant.
Good luck to your and your betta!