This thread has a *lot* of great information on Betta care. You will need a bigger place to keep your new friend in. 2 gallons is a good minimum size. 5 gallons is better since 5 gallons and up can hold a stable cycle. (You can read up about cycling later, for now choosing a tank is all you need to do!)
Here is a thread about water quality: http://www.bettafish.com/showthread.php?t=66595
Bettas are fun fish to have! They don't need a lot of special care, but they do need some things:
Tank of at least 2 gallons in size.
Water conditioner/dechlorinator >> This is a MUST HAVE item! Chlorine from tap water can kill your fish. Prime is a super brand. Very concentrated and it helps to make ammonia and nitrites less toxic to your fish.
A heater >> 80 degrees is their ideal temperature, but 76-82 is fine. You do NEED a heater for him!
Food >> Pellets are the best type of food. Omega One Betta Buffet pellets are a good type. New Life Spectrum is another one people often recommend.
A hiding place! >> A little cave or other aquarium decoration with a place for your Betta to hide will make him feel safe.
A few decorations >> Silk plants are nice. Plastic ones can often tear fins. Always check new decorations for sharp edges!
: (Not needed but nice to have)
Filter >> If your new tank is at least 5 gallons in size, a filter will let you 'cycle' the tank. This will eventually make it so you don't need as frequent water changes. It takes time for the beneficial bacteria to grow in the filter, so a water test kit would be something great to have if you go this route.
Water Testing Kit >> The API Freshwater test kit is great. Pricey, at about $30 in stores, but well worth it since you can test numerous times. The test strips you can buy are not accurate and you usually only get a few in a box.
Live Plants >> These can be planted in the aquarium gravel, or some are free floating. Plants help suck up ammonia and nitrate from your water, and release oxygen. They are a healthy and pretty item for the tank! But, they are not needed and they do need some care. Mostly they need the right kind of light.
This is all I can think of for now. But there is a ton of information here and plenty of great people to help!!