Above is a general schematic of the peer review process.  Each publication has its own individual process, but this illustration gives you a general sense of common elements.

The overarching purpose of peer review is to increase the quality of the manuscripts that get published and try to catch errors, mistakes, fraudulent claims and/or weak research before they get disseminated.

If you are unsure whether a given journal is peer-reviewed or not, visit the journal's website and look at their editorial policies.  Any peer-reviewed journal should discuss their peer-review process in detail so prospective authors know what to expect when submitting manuscripts for publication.

Although the research articles in a scholarly journal are usually peer-reviewed, there are other types of content in those journals that are not peer reviewed.