Basically, a primary source is an original research report. A secondary source is a synthesis of others' work.
Primary source research articles generally include the following: abstract; research question; introduction; literature review; research methodology; setting/context/location; participants; findings or results; discussion; implications or conclusions; and suggestions for further research.
Phrases that might be found in the abstract for a primary source article include "the study findings," "the purpose of this study is," and "the participants were observed for." Phrases that might be found in the abstract for a secondary source include "this review synthesized research," and "in this article, I critique a component of the curriculum."
Here are some resources to help clarify the difference between primary and secondary sources.
Quantitative sources are statistical or experimental; quantitative studies can be generalized and generally do include a methodology section. They authors may refer to participants/subjects and often seek to prove something via experimental and control groups. Specific variables are studied.
Qualitative sources are exploratory and subjective; qualitative studies can be used to anticipate effects and generally don't include a methodology section.
Here are some resources to help clarify the difference between quantitative and qualitative sources.
A peer reviewed source is one where an author's work is critiqued or evaluated by experts in the same field or discipline before being published. The reviewers are examining how this new work contributes to the discipline. Many scholarly journals use a peer review process before publishing an article. If you aren't sure if the journal in which the article appears is peer-reviewed, look at the journal's home page which should indicate if it is peer-reviewed.
In addition to qualitative and quantitative research studies, you might find other primary sources that reference empirial research, ethnographic research, or longitudinal studies. These sites provides brief definitions for each of these, as well as many other concepts in educational research.