You need to identify the record by using an ID, not the field values. If you look to a lot of websites, usually they send the ID to identify a record. Like edit.php?id=1284, or view.php?id=1284, etc.
In short you will have a form that you fill up with the values that are in the database for that record ID. If you edit it, you write a edit query like:
$UpdateQuery = "UPDATE customer SET name = '" . $name . "', address = '" . $address . "' ....... WHERE id = " . intval($_GET['id']);
The reason I add intval is because that will only allow numeric values to pass through. As mentoined by bobince, watch out for SQL injections and let mysql_real_escape_string pass through all of your string values you enter in the query too.