Do you have a pic of the tank and also of his fins?
That would be a great start.
How long have you had him?
The fins will grow back over time if you can get him healthy.
Do you have gravel in the tank?
Sometimes food and waste get trapped in the bottom in the gravel and the snail can't really reach it and the water quality gets bad.
The first thing I would do is take out the snail and the fish into a clean well rinsed container with tank water you get from scooping it out of the top of the tank.
If the snail is stuck on the glass, gently wiggle its shell a bit so it begins to retract and falls off of the glass.
Clean water is one of the best things for a fish, sometimes that is enough for the fins to begin growing normally.
Do you have a filter on the tank?
Next I would clean the bottom of the rocks with the tank water to rinse out any poop or food build up. You want to keep the gravel only being cleaned gently with treated / dechlorinated water.
I would buy him Hikari Bio-Gold Betta food if you don't already feed him that.
Clean out any mess. Only use water, no soap, chemicals, etc.
Refill with treated water after putting the gravel back in.
Acclimating - Take the new water and mix it into the water with the Betta, a few ounces at a time over the next half hour until the water volume has doubled, then take out half of that water dump it out.
Then add back new water to the Betta half new more water and then add the other half more about 10 minutes apart. Then put the Betta and snail back into the new water.
This extra effort will help keep the shock of different water quality to a minimum and the fish will like the new clean water.
Then feed minimally but enough for the Betta and just a little bit for the snail.
Keep up
pwc every couple days through the next 10 days, (maybe 20-30%) do another tank rinse out like before but you won't need to do the acclimating because the water will be very similar to the new water.
If the Betta doesn't seem to be looking better within the first week, you may need to get some other medicine.
You can use the Melafix that is alright. Don't over dose it.
Really clean water is so important.
I would also, if I was treating this add a pinch of aquarium salt and dissolve into the tank, for 1.5G about 1/2 tsp. Although you could add more. I think that would be fine.
If you have any questions or I wasn't clear enough, please just ask, kinda rushing.
If you don't have a filter I would look into getting one.
Also a test kit would be useful to measure Ammonia, Nitrite and Nitrate. I have to get to work so I will answer more questions later or someone else can step in too.
New to FW fish? First tank in a long time or EVER??? Need some info on keeping fish? 
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