In Angry Birds Classic you can use either Rovio Account or Facebook connect to save your progress to the cloud. Once you have signed into one of those, you can access your data from any device that is compatible with the game.
You can access the Rovio Account from the main menu by clicking the cogwheel (Settings) and the account icon.
You can access Facebook connect by opening the Mighty League and clicking the Facebook icon.
NOTE: We have discontinued offering Rovio Account feature during May 2018. Existing accounts can still be used, but new accounts cannot be created.