The 24 hours run time is because that's about how long it takes for the tank to completely cycle all water through it... 12-24 hours. It's a good idea to give you heater that much test time as well before you subject your fish to it. You should watch temps carefully during that time to make sure it keeps a constant temp and that temp is appropriate for your betta. You absolutely need to use an in tank thermometer with any heater: http://www.amazon.com/Marina-Floatin...na+thermometer
Especially one of those preset ones which tend to fail and overheat and/or cause lots of fluctuations. With a tank that size you can get a good 50w heater, which is what I recommend. I like Jager, and Aqueon Pro (not the regular line which are subpar) and Marineland Visitherm, personally.
If you have an HOB I highly suggest using a prefilter sponge so your betta can't get sucked into it.
You will need a drops test kit for ammonia, nitrite and nitrate. A lot of people use this kit: http://www.amazon.com/API-Freshwater...aster+test+kit
Test daily for ammonia and nitrites. Any time you see ammonia or nitrites get to .25ppm you do a water change. In addition to this you do a weekly 50%+ water change. At first you will see an ammonia spike. After that ammonia will go to zero and you will see a nitrite spike. Eventually you will start seeing some nitrates and then eventually both ammonia and nitrites will be zero and you will be left with only nitrates. Those can be removed by weekly water changes. Cycling will take up to 2 months. http://www.bettafish.com/showthread.php?t=47838