ActionScript
Using Facebook Graph API In Flash AS3 To Upload Image And Post To Photo Album — Download Example
February 3, 2011
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Download It (requires Flash CS4 or newer)

The code is in the actions layer on the FLAs main timeline. To use the example on your site, you need to change the APP_ID. The download already includes the facebook-actionscript-api files, located within GraphAPI Source_1_5 folder (you can get the latest facebook-actionscript-api from http://code.google.com/p/facebook-actionscript-api/ but use this version first to make sure it works before changing version).

Read the tutorial