I think he likely has finrot, which is caused by bad water quality :) You need to be doing at least two water changes a week, 1-50% and 1-100%, at the very least. If the vase is closer to 1g, then 100% every other day would be your best bet to keeping him and his fins healthy :)
Also, to BettaRepublic, aging water 48 hours is useless for a 0.75 gallon when you need to be doing water changes daily. Dechlorinator is fine, just use the directions right, it isnt hard to measure it out to use the right amount :)
I dont know what BR meant by the supplements either, but Yes, you should clean his tank twice in a week.
If you think the tank is closer to two gallons, then a 50% and a 100% change each week should do.
If your tank is closer to 1 gallon, then change ALL (100%) of the water every other day :)
You can measure how much water the vase holds (1 or 2g) by emptying it out (with the betta in a holding container) and filling it back up with water using thoroughly rinsed out gallon milk-jugs. :) Count how many jugs it takes to fill it up. Remember to use a dechlorinator, any one will do.
I Agree. Doing those water changes more will help. Use dechlorinator, youll need it.
And try going onto google for us and search for "mild fin rot" and see if it looks like any of those images. If its worse, try just "fin rot" and if worse, "extreme fin rot".
If you find a pic or pics that look like what your fish has, show us the url. We have trouble telling you without a pic if its fin rot, but this way, we can get an idea and helps us to evaluate how to help you heal him.
i age the water for 48hrs, my current fish tank is 0.75g, OFL.
And riese98, bettamin is a supplement, but it should work for now.
.75 is too small. Bettas need at least 2.5, I would upgrade as soon as possible. Also, aging the water may remove some chemicals but definitely not all. Dechlorinator/conditioner is ALWAYS necessary, whether you have a .75 gallon or a 75 gallon.