People are having problems with their treadmill belts breaking up and to be honest it is not very uncommon. Most of the manual treadmills have these problems since the belt is under a lot of tension due to the friction caused by the rolls feeding the belt.
Electric treadmills don't usually have these issues since the engine of the treadmill is feeding the belt and there is not so much of tension in it.
When the belt starts to tear you need to make quick decisions since it breaking in two pieces while running can cause accidents and even injuries that can last for life. If you are a man you are familiar with the easiest way to fix it. Just duct tape it. Adding a good amount of duct tape to both sides of the belt will make it last a long time but you need to keep an eye on it so that it does not start to break again.
The second way that comes to my mind on how to fix the treadmill is to use a material similar to the belt and a strong epoxy glue. The tire of a bicycle can be easily modified to fit small tears and with good use of the glue you can make it look like it never broke.
If your treadmill belt has big tears in it you need to either replace the belt or replace the treadmill. The latter being of course the more expensive option, and also the easier one. You need to measure your belt to make sure that you are getting the correct size, also contacting the manufacturer can help you in this since they are usually selling spare parts. When you replace the belt, make sure that you use enough treadmill belt lubricant to keep it moving smoothly.