Its okay, for now at least, to keep them in that tank. I think I know the very one you have, too. Please, try to get a larger tank to divide (at least 4-5 gallons), or get them separate containers to live in. They need at least 1 gallon of space each, but that is still very, very small. Opt instead for 2-2.5 gallons+.
While theyre together, please change the water at least every other day. This is because, in a small tank with two fish, ammonia builds up very quickly. Ammonia is toxic and can only be removed by live, stemmed plants or by water changes.
Take them out of the tank, put them in the cups they came in, do the water change (all the water, 100%), refill using conditioner, and then acclimate. Acclimation is when you allow the fish to get used to the water to avoid shock, which is deadly. "Bob" their cups for about 5 minutes, and after, add in new tank water to the cups (a little bit) every 5 minutes. This process needs to take at least 15 minutes. Then, add them in, avoiding getting any old water into the tank.
Bettas need space, 2-2.5+ is ideal
Bettas need water conditioner, and not distilled water!
Bettas need a heater- 76-82'F, to live.
Bettas should be fed at least two pellets a day. (no once a week jobs here!)
Bettas need clean water. They need, in a 2.5 gallon bowl, a 50% water change every other day or every two days, and then a 100% change once a week.
(Yours is everyother 100% because there is so much ammonia)
Bettas need acclimation!
To keep stress down, keep the room dark and cover their tank with a shirt until you get a better habitat solution. Thats what Ive done! :)
This is a great tank btw:
I have one, divided: (kinda hard to divide, but not too bad) http://www.walmart.com/ip/Tetra-Aqua...-Pets/12177653
This would be PERFECT for you!!! :)
Very popular on the site:
And yes, bettas eventually (usually) stop going nuts over seeing eachother through the divider, especially when it isnt a clear one. It takes time, though. Keep the tank dark for now.