There are two important aspect to your question.
Are authorized user supposed to be able to delete any record they see fit? If that's the case your issue is one of making sure the request came from an authorized user. In that case using PHP's session is one way of making sure that it's the user you authenticated that made the request. Of course, with all technologies you have to make sure you use PHP session the right way. There are a bunch of articles on that mather. PHPsec.org has one here.
If a user cannot delete any row, in addition to doing authentication and sessions you'll also need to had a check in your code for the verify if the record being deleted can be deleted by that user. Now this is highly dependant on your application. For example, in a project management software, one could be allowed to delete tasks associated with one project but not with another one. That's part of your business logic.
The best would be to perform both check. One, your application must verify if the user making the deletion is a valid user and is allowed to delete (very simple to implement with php sessions) and two make sure that the user can delete the specific record based on some form of ownership.