You won't run MySQL queries with JQuery directly. Set up a PHP file on your server that reads the needed information from $_REQUEST, $_POST, or $_GET (depends on how you want to implement it), then inserts that information into your query and handles the database call.
Once the database responds, you can send the information back to your jQuery app with
echo php_jsonencode($data); //Data is what ever value you got from the database.
That will send your database data back to jQuery as JSON so it's easier to parse.
The details on how you accomplish these steps are very dependent on the information your sending, and what you need to send back. So I can't answer more specifically without more details.