Since you don't say what field you are in, this may not work for you - but I'll describe how I do a literature review in the biomedical sciences. I've tried to be general, so it could apply to other fields, but if you're not in science at all it might not work for you.
The first step to writing a literature review is defining your topic. What is the key question/ concept you are trying to explain or summarize? This can be difficult if you are really starting from zero on a topic, and will probably need to be refined as you work on your review. But it's important to define this at least in draft form before you start.
The second step is coming up with search terms. Begin by searching your question/ concept on Google Scholar or another large database - if it's a biomedical topic, Cochrane Reviews is a good place to start. I'm not sure if there are similar review databases for other fields. Look for a few key papers in the area, read those, and look at their reference lists. Also, record their 'key terms' (usually below the abstract) - these will help you define search terms. Pull relevant papers from their reference lists and repeat. Once you've gone through ~ 10 papers you will probably have a good sense of the type of key words that are important for your topic. Use these terms to build an improved literature search.
Third, you need to actually do the literature search. Your field probably has a database of journals - use this and your search terms to identify all relevant papers over whatever time frame you are interested. You'll probably need to refine as you go, so you don't get swamped with papers. I prefer to go use a systematic search strategy, even if I'm not doing a systematic review, since this removes some subjectivity. This means going through all results, and reading any papers which have titles or abstracts that suggest they may be relevant to your question.
Fourth, you need to read and take notes. Make sure your notes are indexed by paper, so that you always have the citation of the original paper with whatever facts you note down. I find OneNote is a great way to do this, but there are other tools I'm sure.
For me, once I've read 20 or so papers, I usually have a pretty good idea of what the answer to my question/topic is, and what the nuances are. Then it's just a matter of organizing the notes that I've already taken into a rough outline of what I want to say (remembering to keep label all the facts/opinions with their citations). After that, you're ready to start writing, and it's not too difficult since you've already got a good sense of what to write as well as a rough draft in the form of notes.
One important caveat is that you should always re-write all your notes in your own words as you go through the outline converting it into a paper. This way, if you occasionally just copied the original author's text when taking notes, you won't end up with their words in your paper (which would be plagiarizing).