You can sync your contacts with your live account. This will be transfered to the 920 when you sync it with the same live account. Media files can be copied using usb cable with a pc intermediary unless you already have the wp7.8 update on your 900 which shoul allow you to transfer them using bluetooth.
Before you start, ensure bluetooth is enabled on both your 820 and the other phone.
Say you want to share a photo. Now goto Photos>albums and select the photo you wish to share. Tap the 3 dots>share>bluetooth>select device you want to share to. Then you need to accept transfer on the other device.
If you were sharing it with another Lumia 820 or 920, the whole proces could be simplified by using nfc and just tapping the phone together.