Ick is a protozoan parasite, and is extremely contagious. Ick will often appear when fish have been stressed by any number of environmental factors - new additions to the tank, rapid temperature swings, fluctuating water parameters, etc. My personal belief is that Ick is always present in an aquarium environment, but that healthy fish are able to fight it off until they become so stressed and worn out that they are no longer able do so.
Ick symptoms are fairly straight-forward and easy to recognize. Ick will manifest itself visibly as white dots on the fish (generally the spots will start on fins and move towards the body, but not always). The spots will be about the size and consistancy as a small grain of salt. Fish will often "flash" or scratch themselves quickly and repeatedly on objects in the tank in an effort to dislodge the Ick cysts. Some fish will continue to act normally even when infected with Ick, but others will have clamped fins, color loss and lethargy.
Ick is highly contagious, therefore if your betta is in a community tank, remove and isolate him. If you can move him to a tank with a heater, this will make treatment easier and faster - warmer temperatures will cause the cysts to fall off faster, which is the only time that they are vulnerable to medications (when they are not attached to the fish). Turning the temperature up to 84-86 degrees F will not harm a betta for the short duration of Ick treament, and will increase the speed at which the fish will be cured. Do not try to put a heater in a small isolation bowl/jar, as you may end up boiling your fish. If you can't heat the isolation container because it's too small, try to place the container in a warm area of the house and allow treatment to progress at its own pace.
There are a bunch of medications on the market that will successfully treat Ick, which you use is more a matter of how available it is for purchase than anything else. Most medications geared toward Ick treatment contain Malachite Green or copper. Commonly available brand names are: Malachite Green, Coppersafe, Quick Cure, Aquarisol, and Maracide. Pretty much any treatment that says it treats Ick probably will. Be aware the some of these medications are fairly harsh on plants and invertibrates, so make sure you do your homework before treating in a planted tank or one with snails/other invertibrates. Also be aware that stong copper-based medications can eventually lead to poisoning, so water should be changed frequently after treatment to remove the medications, unless you are treating in a container that gets 100% water changes.
Clean water, steady tank temperatures, and keeping your fish happy and stress-free fish are the easiest ways to prevent Ick. If you are adding new fish to a community tank, always quarantine them for at least 2 weeks to reduce the chances of the stressed-out new fish introducing diseases to your healthy fish. Always try to keep the tank temperature as stable as possible - heaters are the best way to do this if your ambient air temperature fluxuates a lot. I've personally found that rapid temperature changes are the biggest culprit when my fish come down with Ick - heat the tank if you're having severe temperature changes daily, and if your tank is too small to heat, buy a larger tank that can handle a heater. As with most of the other diseases, keeping up with your tank maintenance (ie keeping the water clean) is arguably the number one thing you can do to keep your fish happy and stress-free. Do not underestimate the power of clean water.