How can I find "scholarly" research articles, with the aim of looking at what the researcher's objectives and methods were?

Universities and colleges have subscriptions (or a general subscription) to 'scholarly' (or 'academic') journals. In some cases, the journals will be available as paper copies in the college library, but all should be available online via the online research portal to which the college subscribes. Ask your lecturer or tutor how to access this.
If you are not in an academic institution, you can search on Google Scholar (scholar.google.com).
Some research papers listed on Google Scholar are free to download in full. Others will just have the 'abstract' (summary) available to view, and perhaps some other details. In the case of those that aren't freely available in full, a small payment is usually required to download the entire paper. If you identify a paper that looks like the sort of thing you are looking for, it is possible to search for the authors on the internet and email them for a private copy of their paper. They may take some time to respond, however.
If the summary (usually called the 'abstract') of the paper is written in a detailed enough way, you might be able to determine the research objectives and methods from that alone. That would be the quickest most efficient way to choose between papers.
Articles, or research papers, fall into two general categories: review papers and new studies. Review papers review previous papers about the topic of interest and summarize the opinions and findings in those papers in a critical way. Papers about new studies are based on collected data from various sources. This could be numerical data or survey data. The study would have a research question it is investigating. The researchers would identify what resources or data they could examine and collect to investigate that question. Based on what they have observed, researchers then draw conclusions to try to answer the original question.
If you are expected to criticize the paper you choose to look at, the things to look at would be
how sensible the original research question is
whether the resources collected are adequate and unbiased for asking that question (for example, are they collected at random from the target population of interest?)
whether the conclusions are accurate and appropriate (was the best method used for analyzing the data, and was the analysis carried out correctly?)
whether the strength of the conclusions is justified based on the amount of data examined
whether the results are of practical interest (that is, the effects observed are large enough to be important)
Bear in mind that if the paper has been published in an academic journal, it should achieve all of the above, otherwise (hopefully) it would not have been published. Papers are usually 'peer reviewed' by other researchers and experts in the same or a similar field to ensure the paper is of good quality. Even so, many badly conducted studies slip through the net.
The typical format for an academic paper (particularly in the hard sciences) is
hypothesis (research question)
method (how the data, once obtained, will be analysed)
results
conclusions (meaning of the results and an acknowledgement of the results' quality and relevance)
Finally, many research projects find their original hypothesis was wrong. This is still useful, however, because something has been learned from the data. Many researchers also find they did not collect enough data to conclude anything definite regarding the question asked (research in this situation is known as a 'negative' or 'under-powered' study). Under-powered studies in particular suffer from 'publication bias' in that they are not published because they failed to say anything of interest or anything exciting. This is unhelpful because lack of information is still, in its own way, information, but it is understandable because researchers who repeatedly fail to find anything interesting are unlikely to receive a lot of financial support or resources for later work.