Recovering your wallet is simple as long as you have recorded your unique 12 word security phase or made a text file backup. To recover you wallet or switch to a different device download the SatoshiWallet app and in your admin area go to:
Add Wallet > Import Wallet > Wallet Recovery Phrase
You will be prompted to input your 12 word phrase and you will once again be able to access your wallet.
For those using the Chrome Application it is possible to create a text file backup of your wallet. To recover a wallet from a text file go to:
Add Wallet > Import Wallet > File/Text Backup
You will be prompted to select the the recovery text file on your device.