Try using the Inchoo facebook connect. it works like a charm and its free.
STEPS TO USE:
STEP1: goto http://inchoo.net/ecommerce/magento/facebook-connect-magento-extension/
Step2: Download the extension. (It is compatible with CE 1.6.2... have tested it and im using it. You can also check up other usage instructions on that page also)
Step3: Setup Application on Facebook and obtain its App ID/API Key and Application Secret.
Step4: Open downloaded module and copy its contents in app folder
Step5: Also copy the template and layout folders under app/design/frontend/default/default/ to app/design/frontend/yourinterface/yourtheme/ folder
Step6: Open Magento backend goto Configuration->Customer->Facebook Connect, fill in the ids etc, set Enabled to Yes
Step7: Refresh Cache / Reindex All
Step8: Add rel="facebook-connect" anywhere within a button tag or a tag. This can be put anywhere in CMS, static block or templates, and it should open up a popup for Facebook login.
Hope this helps...