If your question is about like
for URL
that you can get this information only for user who authorized your application and granted user_likes
permission. To do so issue next FQL query:
SELECT user_id, url FROM url_like WHERE user_id = me() and url="URL_OF_PAGE"
If your page have an ID in OpenGraph (or you speak about Facebook Page), by querying Graph API for user
's likes
connection:
GET https://graph.facebook.com/me/likes/OPEN_GRAPH_OBJECT_ID
But if you speaking about Facebook Page and Application running in Page Tab, you don't need anything special to get this information since it will be passed within signed_request
(sample php code using PHP-SDK):
$signedRequest = $facebook->getSignedRequest();
$data = $signedRequest['data'];
if ($data['page']['liked']){
// User is liked this Facebook Page
} else {
// User is not yet liked Facebook Page
}