Replacing wireless doorbell batteries is a common maintenance task. The main drawback to wireless doorbells is that they quit working when the batteries go dead.
The first thing to do is check the batteries for both the chime unit and the doorbell button. Replace them and see if this solves the problem. Does it work now? Great, your doorbell repair is complete. No, its probably time to go shopping and select a new unit. You can probably find one to suit your needs for around $25 to $50.
Follow the instructions for the unit you select. One item to keep in mind is that the button and the chime unit have to be within a certain distance to work properly. Make sure that the unit you select will work with your situation.
Another irritating problem with wireless units is your doorbell ringing when your neighbor uses his garage door opener. This is mostly a quality issue. Better quality units have features that eliminate this problem. Paying a few extra dollars may be worth it if you don't want to keep running to the door and no one is there.