Ich (Ichthyophthirius multifiliis) is a parasitic infection that spreads from fish to fish. The little white spots you see on the fish are actually embedded parasites. The parasites can also live in your tank - on the gravel, the plants and even in the water. If left untreated this infection will lead to the death of your fish, and will likely spread to any other fish in the tank.
There are over-the-counter treatments for ich, but many aquarium owners rely on raising the water temperature and dosing the tank with aquarium salt. The warmer temperature accelerates the lifecycle of the parasites, and the salt kills them off. Unfortunately, most treatments are somewhat stressful for the fish. You’ll want to do some research into the different methods of dealing with ich and decide which is best for you.
If you have had a string of betta fish die from ich, I am going to assume you had them all in the same tank, one after another. The tank is now infested with parasites, and any fish you introduce will be vulnerable. If you have no fish in the tank, you need to tear down that tank and thoroughly sterilize it before attempting to keep more fish in it.
I would drain the tank and remove all of its contents, (make sure you unplug any electrical items first!) then clean the glass and the filter with a strong solution made with water and aquarium salt, making sure to rinse thoroughly when done. I'd replace the gravel, the heater and all of the decorations, along with all of the filter media with new items. You will need to re-cycle the tank before adding fish.
When you do introduce a new betta, make sure you are keeping his tank conditions under control. When tanks become dirty, and water conditions deteriorate, it is stressful for the fish, and their immune systems suffer. This makes them more susceptible to diseases like ich.