Use the open graph API. Here is a live example querying how many likes "Coca Cola" has.
https://developers.facebook.com/tools/explorer/?method=GET&path=cocacola%3Ffields%3Dlikes
Which boils down to:
https://graph.facebook.com/cocacola?fields=likes
Which you could do in an AJAX GET
The result is:
{
"likes": 71717854,
"id": "40796308305"
}