Your question is pretty vague. I don't use facebook, I've no idea if you host some sort of web based game on a site, or wish to find results of a game hosted elsewhere. If the latter contact the people running that service and find out if they have an method of querying their system (API). If this isn't what you mean please provide an actual question.
Update: Please mark updates you make to questions. I don't see where scores are recorded in the google doodles. You're going to have to ask an actual question.