if it is ragged looking along the tear he may have torn it on something in the tank, a plant or something. Have a good look around his tank, a rule of thumb for ornaments is to run a piece of pantyhose over things, if it catches it may tear a caught fin.
Another common fin damage problem is a blowout, caused when they flare so hard their fins split, these usually look nice and clean along the tears, like someone ripping a tear in a piece of fabric.
For healing really all they need is nice clean water and (if you have it on hand) indian almond leaf. Betta fins are suprisingly durable and will grow back from just about anything. first looking white or clear and gaining its old color later on when the new fin is strong enough.
By the sound of it it isnt fin rot or some other concern so medication isnt really needed, many people add a little aquarium salt to help heal external injuries, but as long as the water is clean and warm he should grow it back no problem
Edit- having another look at the shots they may be horseshoe shaped? if so they may be bites. a betta version of nail biting. this can come from stress, boredom or just because. It will heal too, but the trick with biting is finding out why the fish bit in the first place or it may keep happening
Last edited by Taeanna; 08-31-2013 at 04:03 AM.