Instructions
Start the game and play as you normally would. It is better to complete most of the main levels in the game first so that you can become familiar with the gameplay elements.
Complete the levels with enough points to get a three star rating. To accomplish this, you need to use as few birds as possible to cause as much destruction as possible to the pigs and objects on the level. Once you have completed every level on an episode, you'll notice that you unlock something called the "Golden Eggs."
Return to the "Episode Select" screen and click the "Golden Eggs" button below the episodes. This will take you to a screen that shows the available puzzle levels. Each golden egg that you discover will unlock one new puzzle level on this screen. The glowing golden eggs are puzzles you have not yet tried, while the ones with a star on the egg are ones you have finished.
Look for golden eggs hidden away in backgrounds of menus and help screens in the game. You'll find one at the end of the games credits, one on the fourth page of the help screen, inside the sun displayed on the background of the episode select screen and on the last page of the level select for the episode "Danger Above." All of these will add additional puzzle levels for you to play.
Return to the levels you've already unlocked during the episodes and look for golden eggs hidden in the backgrounds. Destroy objects using your birds to find some of them, such as the beach ball on Level 2-2 of "Poached eggs" that is in the middle of the level between glass blocks. Just be on the lookout for anything that looks out of the ordinary and launch your birds at it to see if it breaks. Look for eggs hidden in plain sight as well and hit them with your birds to unlock more puzzles.