Return Array from Function in Swift

The graphConnection.addRequest is an asynchronous function and you are trying to synchronously return the array of strings back. This won't work because the graphConnection.addRequest is done in the background to avoid blocking the main thread. So instead of returning the data directly make a completion handler. Your function would then become this:

func fbGraphCall(completion: ([String]) -> Void, errorHandler errorHandler: ((NSError) -> Void)?) {
    if (FBSDKAccessToken.currentAccessToken() != nil) {
        // get fb info
        var userProfileRequestParams = [ "fields" : "id, name, email, about, age_range, address, gender, timezone"]

        let userProfileRequest = FBSDKGraphRequest(graphPath: "me", parameters: userProfileRequestParams)

        let graphConnection = FBSDKGraphRequestConnection()

        graphConnection.addRequest(userProfileRequest, completionHandler: { (connection: FBSDKGraphRequestConnection!, result: AnyObject!, error: NSError!) -> Void in
            if(error != nil) {
                println(error)
                errorHandler?(error!)
            } else {
                var fbData = [String]() // Notice how I removed the empty string you were putting in here.
                // DEBUG
                println(result)


                let fbEmail = result.objectForKey("email") as! String

                // DEBUG
                println(fbEmail)

                fbData.append("\(fbEmail)")

                let fbID = result.objectForKey("id") as! String


                if(fbEmail != "") {
                    PFUser.currentUser()?.username = fbEmail
                    PFUser.currentUser()?.saveEventually(nil)
                }

                println("Email: \(fbEmail)")

                println("FBUserId: \(fbID)")

                completion(fbData)
            }


        })

        graphConnection.start()
    }
}

I added the completion handler and the error handler blocks that get executed according to what's needed.

Now at the call site you can do something like this:

fbGraphCall( { println($0) // $0 refers to the array of Strings retrieved }, errorHandler:  { println($0) // TODO: Error handling  }) // Optionally you can pass `nil` for the error block too incase you don't want to do any error handling but this is not recommended.

Edit:

In order to use the variables you would do something like this at the call site

 fbGraphCall( { array in
      dispatch_async(dispatch_get_main_queue(), {  // Get the main queue because UI updates must always happen on the main queue.
             self.fbIDLabel.text = array.first // array is the array we received from the function so make sure you check the bounds and use the right index to get the right values.
             self.fbEmailLabel.text = array.last 
      })
 }, errorHandler:  { 
        println($0) 
        // TODO: Error handling  
  })