The Facebook Connect documentation is rather limited. It doesn't really tell you what it is doing, only how to do it. I personally don't use either SDK. I have built my own framework for my development projects.
Both SDKs as well as the JavaScript in the tutorial are, IMO, fairly outdated.
If you want to stick to one of the FB SDKs here is my suggestion. Use the JS SDK only if your Graph API queries and the like are sent to a PHP backend via Ajax. Otherwise stick with the PHP SDK.
Introduction
Facebook uses oAuth v2. They describe two different methods of flow... Server side and client side. This would be implemented just the same as any other application authenticating against an oAuth v2 service. They both do the same thing. The only difference may be you can use 'code' as a request_type to get an authorization code for obtaining a token in the future.
Authentication
As far as FB Connect is concerned ll your script needs to to is make sure you have an auth token or auth code whenever you require authentication. If you don't have that then you need to get it. You can use the presence of an auth code or token as a condition for which FB button to show (login or logout).
Redirect the user to oAuth for authentication. Facebook has their oAuth implementation bundled in to their dialog API. More information on the oAuth Dialog here: http://developers.facebook.com/docs/reference/dialogs/oauth/
You can use the optional state parameter for something such as CSRF protection. It retains it's value after the process and is sent with the callback as a GET parameter.
Application Interaction
Basically you're going to write your application the same way you normally would. The differences would be:
- Your user database no longer stores a password, just the FB UID. Also, according to the FB Dev ToS you really can't store any user information. If you want to store user information you need to get it from the user. You can populate this information for them with FB information, you just need them to submit it.
- Your registration method won't have a form frontend posting to it any longer. It will be called when an authenticated user does not have an entry in the DB.
API Interaction
If you went with code instead of token you need to request a token by sending code. This is done with the Graph API oauth. This part is not documented at all other than in their authentication tutorial. http://developers.facebook.com/docs/authentication/
With your access token, whichever method you may have used to obtain it. You can now query the Graph API however you desire. This will return a JSON encoded object.
Conclusion
As far as a fast and secure implementation goes, the Facebook PHP SDK does the job. It handles everything I covered here, including the CSRF. How to go about learning it, I have yet to find decent documentation on it. Everything is either old or the writer doesn't really know and is going off of other tutorials.
Your best bet is to dig deep in those libraries and figure out how it works for yourself. Do some trial and error, experiment.
The way I learned was by writing my own framework for it. I suggest you do the same. You can extend the Facebook SDK classes if you like. It's really limited, but it gives you all you need. I took my most commonly used API calls and placed them in as well. I now have a very quick and simple end result that is driven from my library.