That is a rather sorry looking boy, but with the right steps I also think he can be saved. If that little vase/cup he's in is his "tank" then that is probably the first issue. Bettas are fish, fish need tanks, tank=filter+heater. The temp should be around 80F give are take a few as bettas are tropical fish. A 5gal tank kit isn't all that expensive and will provide all you need for a happy betta.
The tips of his fins are the beginning of fin rot due to poor water quality. I would imagine the nitrites and ammonia are quite high in his vase/cup. You want both to be zero. I suggest you look into the Nitrogen cycle.
He is also a bit bloated, don't feed him for a couple days and that should fix it. Also decrease the amount of food he gets. 3-5 pellets a day is a good amount.
So what it comes down to is this. He needs a larger home with a filter and heater. That odd mark/coloration on his tail base might be an infection of some sort and should hopefully clear up with better water quality.
BTW the first thing I'd be doing is filling up a clean bucket with and moving him to it. Something like a large Tupperware dish will work. He simple needs to have clean water ASAP. Just make sure the temp is the same as his water before moving him.