How can a student be able to find open access journals with no publication fees to publish their work? A step by step procedure will be most appreciated.
Very easy. Usually, DOAJ can be considered as one of the fine whitelists available to find legitimate OA publications. However, even this may include low quality journals, but you will be able to identify them after examining the information on the official websites of these journals. DOAJ includes information of journals (articles too) and you will be able to retrieve journals and their information following a number of search strategies. For example, if you need to see the details of journal X indexed in DOAJ, you will be able to retrieve its information through the browsing facility based on X's subject domain. This process will retrieve information like publisher, APC, submission charge, processing time, copyright, and so on in a single window. Therefore, you can very easily check whether the target journal includes a publication charge (APC and submission fee).
The best standard alternative is to try to publish in a very good journal, without the OA option, and simply rely on that your university has a subscription!