How do I orient myself to the literature concerning a research topic and not be overwhelmed?
Start with well-written review papers. These are designed to do exactly what you ask: to orient a reader to the state of knowledge in some field. If you are working on something multidisciplinary you may need a separate orientation for each discipline if there isn't a good review that already makes the connection for you.
Then, once you are oriented, you can start to dig. Try to discipline yourself towards pursuing a specific goal in your literature search. When you find offshoots, label them as future places to dig but don't start excavating them quite yet.
Other than that, try to stay organized. Organize your thoughts by writing down what you are learning, make concept maps if they help you, or start organizing references into nested bulleted lists. Be open to reorganizing as things develop.
I want to add an addendum concerning your specific field of research. Published science in biology and medicine, and even more so in areas related to mental health/psychiatry/counseling, may contain a lot of conflicting information. These fields deal with some of the most complex systems humans know of, and our core knowledgebase is extremely lacking. If you're used to reading textbook descriptions of "how things are", the actual academic literature is by comparison extraordinarily muddy (this is true of all fields, no doubt, but I think especially the ones I've mentioned). It may help to know to accept this, and to not treat any one paper as Truth. There are competing models and competing hypotheses and competing approaches to treatment because none have yet "won".
Adding from a comment: if you are wondering how to find review papers...
There are some journals that only contain reviews. Some of these are good journals (and since reviews tend to get cited a lot, you can often discover them by their very high impact factors), some are not (these will tend not to be cited much). Some indexes, like PubMed, allow you to filter for only reviews (I don't know how accurate these filters are). Otherwise, adding "review" to a search string will help. You won't get all reviews, but many of the top results will be.
The first answer by Bryan Krause is excellent. I only add a few points.
- Apart from review papers, also good contemporary papers that are close to what you are interested in can give you some orientation by how they survey the literature in the introduction and maybe in some more specialist parts connected to what you want to work on. This will also give you an idea how much the experts think should be taken into account (note though that often papers are cited that those who cite them have not fully read - maybe they just had a very quick look and have decided that this serves as a reference for a specific issue they want to highlight).
- It is important to acknowledge that there may be so much literature that is related in one way or another that the task of reading and understanding all would be too much to ask for everyone. Even the top researchers ignore some stuff, just because they have to, there's too much out there. A good attitude could be to restrict oneself to a well defined small "subproblem" and to consciously take some things for granted that are backed up by good recent literature. It is important to define limitations of the area of interest and to leave some issues out (and rather stick to one position that is taken by some literature even if some others disagree with that), but at the same time to not forget there is more and to remain aware of the limits of the approach you are taking. You don't need to present your material as if you knew everything, you can say things like "there are other approaches but I don't consider them here; they could be topics for further research". Sure, you may miss something important, but with a modest enough way of presenting/writing, whenever somebody makes you aware of what could be beneficial to take additionally into account, you do not have to defend that this was ignored but can rather say, "thank you, good hint, I'll have a look at that". Surely at masters stage and early in the PhD, people should understand that you can't know it all.
It can also be useful to quantitatively analyse the literature from the information in databases such as scopus. For example, a few lines of code in the bibliometrix package in R (I'm sure there are alternatives) can tell you the most cited authors, papers and other useful info very quickly. If you have the time you can even take this a step further and look at the whole citation network that shows you clusters around research groups.
It can also be helpful to keep track of search terms you have used and also to tell databases to notify you of publications that contain some keywords as they are published.
This is more targeted at your first question in addition to the answers already posted :)