Most (if not all) of your peer reviewed academic sources will be articles published in scholarly journals. Start your search with the library's Discover service. If you don't find what you need (or if you are just the sort of person who really likes to do things thoroughly) try some of the library's scientific databases.
Remember that you are looking for research articles. Scholarly journals mostly publish research articles, but they also publish things like editorials, letters and book reviews, which are excellent sources (and would satisfy the requirement for a non-peer reviewed academic article) but may not satisfy the requirements for this part of the assignment - because even in a peer reviewed publication, these other types of writing do not always go through the peer review process.
For an article to be considered peer reviewed, it must meet all of the criteria for an academic source, plus the one more:
A. The author is an expert in the field who is paid to do the research.
B. There is a bibliography.
C. There are in-text citations.
D. The article has been reviewed by one or more of the authors' peers (i.e., experts in the same or a closely related field).
A. Is the Author an Expert?
Someone is an expert in a field if they are paid by a university, government or other institution to do the research. Scholarly articles will almost always give the authors' affiliations -- i.e. who they they work for -- at either on the top or the bottom of the first or last page.
B. Is there is a bibliography?
A quick scan should answer this. Remember that "references" is another world for bibliography.
C. Are there are In-text Citations?
Again, a quick scan should determine this.
If you have found EVIDENCE for a, b, & c, then you have an academic article. Now you just need to confirm whether it is a peer-reviewed source.
D. Is there evidence that the article has been reviewed by the authors' peers?
There are two kinds of evidence that an article has been peer reviewed. One form of evidence is dates on the article itself indicating when it was originally received by the journal, when it was revised, and when it was finally accepted for publication. If there is just an "accepted" date, then you don't have sufficient evidence that it actually went through peer-review prior to publication.
If there is insufficient evidence on the article itself, then you will need to search online for the journal's editorial policy. Often this will be on the publishers website under the Aims & Scope section or the Instructions for Authors section.