I could talk for pages about betta enclosures, and I will later. Having a good setup makes having a healthy betta much easier.
For now, if it's under 1 gallon, get a bigger one. If it doesn't have a heater, get one (that's not the Aqueon betta bowl heater). If it doesn't have fake plants (the kind that aren't too scratchy) and a cave to hide in (terra cotta pot on its side works well), get that too.
Quick few myths, busted: Plants don't filter your water. Snails and shrimp don't filter your water. If you have a filter, you still need to change your water regularly. There is no maximum size for a betta tank, as long as there aren't too many big open spaces.
Food: Bettas are carnivores and can't digest plants. Because of this, you should find a food with a high meat content and a low grain/filler content. I feed my fish Omega One Betta Buffet, because it's got quality ingredients and is available at petsmart.
Because your betta will crap out all the non-meat parts of their food, feeding a pellet that's high in meat and low in fillers will make your fishy poop less, which is important to keep in mind if you have a smaller or unfiltered enclosure.
One of the top betta killers is obesity. Also, if you feed too much, the uneaten food will sit on the bottom and foul up your water. Pellet size differs between brands, but if I smush all the food I feed in one feeding together, it is about the size of half a pea. Their stomachs are about the size of their eye. With Omega One sized pellets, I feed four to six pellets, once or twice a day.
You can suck uneaten food off the floor of your tank with a turkey baster (one that is kept exclusive to fish and not used for cooking).
Water: You can't use the water out of your tap without treating it. Water conditioner is cheap and works almost instantly. I use Seachem Prime because it's very concentrated, but I also use Tetra AquaSafe/BettaSafe, because it's readily available. Stress Coat+ has aloe in it, which is good if you've moved your fish or if he's sick, but it's also expensive.
Prime also can detoxify ammonia for short periods of time, so I add about 2 drops per gallon every other day in an unfiltered tank. This does not replace the need for weekly water changes.
Betta can adapt to a wide range of PH and KH levels, so don't worry about trying to change them. The chemicals available for changing your PH are actually pretty bad for bettas, because it makes an unstable PH, and they need a stable PH more than they need the technically 'correct' PH.
If you're really concerned about a high PH, adding a piece of driftwood to your tank can help, and looks pretty.
Water Changes: Water changes stress your fish, so it's important to not do them more than necessary.
If your tank has a filter, you don't need to change out all the water. On a 5-gal tank I change about 1/2 the water every week or every other week. On my 20-gal that has 4 betta in it. I change about 1/4 of the water every week or every other week.
If your tank does not have a filter, or is under 2.5 gallons, you have to change all the water every week. You cannot skip a week, and being even a few days late can have bad effects. In a 1 gallon tank, I suggest changing the water every 5 days.
If you want to know FOR SURE when you need to change the water, pick up a liquid ammonia test and test your water daily. If the ammonia level reaches .25, change your water. If your ammonia level doesn't reach .25 in a week, still change your water, because your level of dissolved solids will be pretty high by that point.
If you have a filtered tank, use a liquit nitrate test kit. You need to change bi-weekly or when your nitrate level reaches 40, whichever comes first.
To do a partial water change on a filtered tank, use a siphon and a bucket dedicated to fish. I like the kind of siphons with a priming bulb, and I like the 5-gallon bucket I got at the hardware store. Use the siphon to clean the gravel in your tank too.
To do a full water change on a small tank, start by getting the fish out of the tank and into a cup (the one he came in will work well). I don't use a net, I just scoop with the cup. Then dump out all the water, rinse out your bowl, fill the bowl up with water and dechlorinate it. After the bowl's halfway full, add your rocks and plants back in. If you add your rocks before your water, you can break your bowl if it's made of glass. I find that larger, marble-sized rocks work better than pea gravel for unfiltered tanks, because they're easier to dump out and put back in.
On my 2.5 gallon unfiltered tank, I leave my fish in and siphon the water down to as low as I can go without upsetting the fish, and then adding in dechlorinated water.
Always try to match your water temperature with the temperature of the water the fish was in. Be careful not to add too hot of water--remember, 82 degree water (the max temp for a betta) will still feel cool on your wrist. After a while, you'll be able to judge the temp by feel, but for the first month or so, use your thermometer to check.
Some people will tell you to do 100% water changes every day for unfiltered tanks. I find that the stress of changing the water every day doesn't outweigh the consequences of living in a low-level ammonia environment, and that twice a week is sufficient.
That's all I've got for tonight, so let me know what else y'all'd want in a care sheet and I'll add it.