Peer review is, "The procedure by which academic journal articles are reviewed by other researchers before being accepted for publication" (Arms, 2000)
1. Arms, W (c2000) Digital Libraries, M.I.T. Press. 
All journals will outline their reviewing policy in the journal, or on the journal's website.
All authors should ensure that they abide by guidelines set by the editors and remove any identifying information if requested for peer review. For example, ensure to remove your name, affiliation, initials etc from:
These are all obvious, but can be easy to overlook!
Young, Jeffrey R. (2006). Microsoft Word's Hidden Tags Reveal Identities of Once-Anonymous Peer Reviewers. The Chronicle of Higher Education. April 7 2006, 
Beatty, J. (2002). Removing Personal Data from Office Documents (Anonymizing).
You don't necessarily need to be a long-standing member of the profession or a subject expert to be a peer reviewer for a journal or publication. Journals will outline the criteria for becoming a reviewer in the journal, or on the journal's website. Many journals will welcome new reviewers and assist with completing reviews. Alternately, conferences can be a good place to begin reviewing.