Hi, welcome to the forum and the epic world/obsession with bettas. :D
The water thing (cycling) is really easy. I'm going to make a long post basically touching on all the suggested requirements, so if I repeat anything you already know, forgive me :)
Feeding: 2-3 betta pellets twice daily, 6 times a week (7th day is a fasting day). The pellets must have some sort of meat (fish meal, shrimp meal, etc) as the first ingredient. Before feeding, soak them all the way through.
Tank: Minimum of 2 gallons, must have a heater that keeps your tank at a constant temp between 76-80 degrees fahrenheit, and have proper water changes. Water changes vary depending on size and if your tank is cycled or not. (I'll get to that in a moment).
Compatability: Females are just as agressive as males, keep all bettas seperate (unless in a sorority-which is a risk). No tank mates are advised for anything less than 5 gallons. Shrimp and snails good for 5 and up. 10 gallons and up are alright (depending on the temperment of your betta) are alright for one small school of fish. Tank mates are at risk of getting hurt by your betta and or eaten.
Cycling: Basically cycling is putting some sort of ammonia into your tank. The ammoina gets converted to nitrItes, which are then converted to nitrAtes. Of the three, nitrAtes are the least harmful to your betta and can be tolerated in higher quantities - thus the reason you can get away with less frequent water changes. Cycling fishless is advised, and can take about a month if the tank is not seeded (Seeding a tank is taking something that has been in a cycled tank and has the benificial bacteria on it, and sticking it in your tank- basically expanding on an already living colony of good bacteria).
When cycling fishlessly, you can use fish food (which decays and excretes ammonia), pure ammonia, or raw shrimp (which decays and excretes ammonia). Shrimp and fish food are easy, but messy. Shrimp is probably the easiest, you just toss in a shrimp (in a mesh bag or pantyhose) and let the tank cycle. With fish food and pure ammonia, you pour in the required ammount once an day every day.
After a while, you will see your tank parameters will change, and you'll find that ammonia rises, then falls. NitrIte rises then falls. NitrAte rises. When it rises past 5ppm, you do a huge (50-70%) water change, and your tank is cycled.
While cycling, it is necessary that you have a filter running 24/7. The filter airates the water and keeps the bacteria that make the conversions alive. Not to mention that the benificial bacteria live in your filter... Also, a good liquid testing kit is advised. The API Master Test Kit is the best, which you can get from Walmart for 20 or so dollars (half of what the petstores sell them for).
Anyways, for cycling, here is an awesome link (complete with pictures :D ) http://www.fishlore.com/NitrogenCycle.htm
(cycling in a nutshell: 1) put ammonia source in. 2) watch and wait. 3) watch ammonia rise and fall 4) watch NitrItes rise and fall. 5) Watch nitrAtes rise 6) water change 7) Done!!)
**** it isn't advised to use PH up or PH down, just FYI