Navigate to the downloads section of this site and click the DigiByte Android wallet link to be taken to the Google Play store to download the wallet.
Navigate to Settings -> Backup Keys and follow the instructions to backup your private keys. This is how you recover your DigiBytes if your phone is stolen or lost.
It is important that YOU MUST password protect your keys with a unique password. DO NOT use a password you use for something else. Store your keys in a secure offline storage area. DO NOT USE email to backup yours keys.
If some of your transactions are not showing go to Settings -> Reset Blockchain, reset the blockchain and wait until the chain has resynced. Your DGB will be there.