I think Beta fish are kind of notorious for not always making it. Our school carnival gives them as prizes every year. We've had two that died within a week, one lasted 6 months and two that have almost 2 years. I've heard the same thing from other people, although I think my husband accidentally killed the first two.
Here's what I know:
-Feed them a pinch of food every other day.
-Don't use water straight from the tap. Buy fish tank water at the pet store OR get a little bottle of water conditioner and add it to tap water that's been allowed to sit for several days. (We have a rotating gallon of water that sits in between weekly tank cleanings.)
-Clean tank every 7-10 days. Hubby uses Dawn with bleach. (I don't have anything to do with this, but rinse well!)
-We have a little filter hose or something in our tank. Nothing big.
Also, be careful of decorations you put in the tank. My son wanted a plastic rock. When we washed it, it smelled strongly of chemicals. My husband used it--the fish died. Another one we bought smelled strongly of chemicals, too. Washed it numerous times...smell never went away so we threw it away...the fish lived.
Ask the people at your local pet store and/or get a book at the store or library. Have fun!