I need to use peer-reviewed articles in my assignments and I don't know where to look in order to find out whether specific articles are peer-reviewed.
The articles published by major publishers such as Springer, Elsevier, Wiley, Taylor and Francis, Wolters Kluwer, Cambridge University Press, Sage, De Gruyter, and Oxford University Press are mostly peer reviewed. You can simply search in different databases such as Scopus, PubMed, and Science Direct and look for the articles which are published by these publishers. Once you find relevant articles, check the journal that published those and you will know if the article is peer reviewed.
Kate - as well as Ahtisham's advice - look to the scope and author advice of all journals on their main site. They will usually explicitly advise you as to the review process of the journal. If it is not clear at all - suspect that it may be a 'predatory' journal. Even then, they often state that they peer-review - but it may not a rigorous or robust process. The warning signs will be there i.e. asking for 'up-front' payment before review and/or there is no real review feedback before acceptance.
Look at the publishing processing in the journal website. It must tell if the journal is peer reviewed. Some journals though, are predators, so you may check that as well through the list of predatory publishers.
Some Publishers likee MDPI nowadays also publishes REVIEW REPORT along side with the article. They give the option to the authors to chose if they want their articles to be published as open review article or not and they also give the reviewers the option to be Anonymous or revealed their names at the end of the review process. I think with this you can easily recognize if the article is peer reviewed and can even consult the reviwers' comments.
First, one can check the official website of the journal. 'About this journal' usually explains the peer-review status/procedure of most of the journals. One can believe this if the journal is published by a reputed publisher. However, since there are plenty of scam journals, this is not sufficient for unknown journals. So, check where they have been indexed and from which databases you can find their abstracts. Major abstracting and indexing services usually have their own criteria for selecting journals to include in their databases. This leads to avoid inclusion of predatory publication outlets.
I usually check the quality and the rank of a journal with this website: https://www.scimagojr.com/journalrank.php. In this website you can find many useful information about the journals. I hope if you choose Q1, Q2 or Q3 journals they should be peer-reviewed journals.
But within Researchgate itself, there seems to be no verification link that a journal or article is actually peer-reviewed, correct? If so, is that something that we will see in the near future?
You can check the journal impact factor (IF) published by the Institute for Scientific Information (ISI) . The journals can't have IF on ISI if they don't adhere to some editorial standards, and peer review is one of them. I think this is the only safe method, as there are many predatory journal that claim to perform peer review (and IF!) but in truth they will accept any manuscript with no review. See this useful link: https://openscience.com/how-to-get-impact-factor/