Given the state your device is in you have already erased your old stuff. You have an image on the screen that says, "Connect to iTunes." That's what the image means. So you will need iTunes on your computer.
Upgrading iOS
1. How to update your iPhone, iPad, or iPod Touch
2. iPhone Support
3. iPod Touch Support
4. iPad Support
a. Updating Your iOS from iOS 5 or Later
Tap Settings > General > Software Update
If an update is available there will be an active Update button. If you are current,
then you will see a gray screen with a message saying your are up to date.
b. Resolving update problems
1. iOS - Unable to update or restore
2. iOS- Resolving update and restore alert messages