Hi Shelby and welcome to the forum. What a pretty crowntail.
Here are a few tips for you:
Water changes: one 25% and one 50% change a week if the tank is cycled. 25% and 75% if it is not.
Fin rot IS a bacterial infection and it looks like your little guy has it. If you have live plants, you'll want to treat him in a QT container like a small bowl or cup or a Gladware because aquarium salt will kill live plants. Plus, the smaller container makes it easier to do the required daily water changes.
Fill his container partway with his old tank water. In a gallon jug or container, mix up one gallon of dechlorinated water and one tsp of aquarium salt (dosage is one tsp per gallon). When the salt dissolves, fill his container the rest of the way with the mixture. Float him in his tank so he can stay warm. Temps of 82-84 degrees are good. Change the water in his container every day and redo the salt mixture. If he has not improved after five days, increase the salt dosage to two tsps.
If he gets stressed in his small container and you don't have live plants, you can treat him in the tank. Do a water change first, then add six tsps of salt. You will still have to change at least 75% of the water every day and redo the salt, being careful to only add salt for the water you're putting back in. ie, if you take out five gallons, put in five tsps of salt.
I hope the little guy gets better soon. Keep us posted!