Battery life for your Things varies depending on how you use them. SmartThings' first-party devices (e.g., the Samsung SmartThings Arrival Sensor, Multipurpose Sensor, Water Leak Sensor, etc.) are not rated for outdoor use; using them outside of your home, particularly in harsh weather, can reduce battery life significantly.
Generally speaking, your SmartThings devices' batteries will last anywhere from 6-12 months—again, depending on how you use them.
The type and number of batteries required depends on the device. All of SmartThings' devices have batteries included. For more information about a particular SmartThings device and its battery requirements, go here.
Samsung SmartThings Hub (Hub v2)
The Samsung SmartThings Hub (Hub v2) comes with 4 AA batteries. Once installed, these act as a battery backup that is expected to last up to 10 hours.