If they are running the iOS 5 operating system or later, when the device is powered on, you should just be able to go through the steps on screen (i.e. language, location services, Wi-Fi network, etc.), without the need for a computer. For more info on setup and getting started, see here:
Getting Started and Get-Started Apps
If you have iOS 4.x or earlier, and you see only a "Connect to iTunes" screen, then you need a computer with iTunes.
(Note that I am a representative of the organization for the above link, which is not endorsed by Apple)