How should I ask for library services for literature review? Early on the research planning process, I would like to make use of the services offered by public libraries. Including online library services, what is the best way they could help a student researcher who is currently preparing a research proposal for a specialization? 

Would it be wise to send them an email or give them a phone call, so that they could come up with a list of possibly useful and related research papers at their disposal?
I don't believe that a public library would be a useful resource for an academic literature review.  You are likely to be better supported by a university librarian.  But, I am not sure why you would be relying on a librarian to assist with obtaining resources for a literature review.  My recommendation is that you develop the skills and knowledge to efficiently and effectively conduct a search for relevant resources, as opposed to relying on somebody else.  You presumably have more background and knowledge in your substantive area, and this is something you will be doing throughout your academic career.  Even if a librarian or somebody else culled sources for you, the burden is still on you to ensure the review was comprehensive.