Yes, it is highly advisable to do this. If you are going to do it, choose a study that is relevant or somewhat similar to your research. Talk about the positives and negatives of that study and use that as grounds to avoid pitfalls or issues within your own research. In doing so, you are showing that you are aware of the limitations of other studies and potential ways to avoid issues within your own research. Reflect critically and compare.
Part of the answer depends on the length of your manuscript. For a thesis or dissertation, where you have plenty of room, a brief description of the methodology before describing the findings of the researcher is appropriate.
In a journal article, the conclusions based on the findings are the most important thing in your literature review.
The biggest failing in researcher papers I review is that they have long literature reviews, long methods sections, long findings sections, and superficial discussion sections. Whatever your target length, be sure to reserve room for a rich discussion section, to explain what your findings MEAN and how others can use them.