What are the best ways to write a literature review?

I don't think best way is an appropriate or helpful way of putting it. Rather, literature reviews should be comprehensive, covering the topic’s history, key concepts, influential figures and notable developments. As well, they shouldn't shy away from contentious material. Rather they should attempt to persuasively present data and arguments for or against certain interpretations. This broad umbrella accommodates a variety of writing styles and analytical approaches.

Some examples may help explain the process. For e.g., a while back I wrote an answer about possible human- Mycobacterium tuberculosis co-evolution, Tirumalai Kamala's answer to What if Mycobacterium tuberculosis evolved as a cohabitating organism within the human body?. Like many of my Quora answers, this too took the form of a review so it may be a relevant example.

How to start? Start with what I call a hook. As simple as searching for Human Mycobacterium tuberculosis co-evolution in Home - PubMed - NCBI. In this particular example, I got 24 search results (see screenshot below). Several good leads (outlined in blue), i.e. hooks to get into the subject.

Got those papers, read them, looked up their references, looked up the papers that cited them. Read the abstracts to decide whether to download or not. Doing this builds up a database on the topic rather fast. Once done screening and collating this database, I can sort them into different bins according to subject matter (see screenshots below). In this particular example, I ended up with a database consisting of 9 papers I catalogued as General, 2 as Bottleneck, 15 as Canetti, 4 as Co-evolution, 2 as Deletions, 3 as M. africanum, 7 as M. bovis, 4 as Methods, 15 as Paleopathology, and 3 as Virulence Definitions, for a total of 64 papers. Not a thorough up and down, front and back dredging of source material by any stretch of the imagination. Answer intended only for a general, not specialist, audience after all but this is an example of the basic skeleton required for assembling the database needed for a literature review. As I go through this bunch, the answer starts to shape itself into existence and I start whittling the pile. What's useful? In this particular example, my shorthand for papers I cited have a green dot while ones I found useful for references have a blue dot (see screenshots below).

A similar process attends just about any kind of research I undertake. Cataloging and sorting plus a common file-naming system helps tremendously in gaining control over the reading material, and brings order to what starts out as utter chaos.

Another invaluable helper? Keyword search through a database using Command+F. Helps both with the binning process as well in mining the database for the portion of the answer dealing with a particular keyword.

Process is simple and straightforward in theory. In practice, it requires genuine unflagging interest, and tremendous focus and discipline. Certainly not for the faint-hearted. Especially the citation search. Often papers are cited 100s, even 1000s of times. Trawling though such citations requires a hardy stomach and a spine of steel. Of course, checking each and every citation isn't mandatory nor required for each review. Time and practice helps develop judgment regarding when to pause to pick up another reference or to move on. As well, I tend to read very fast so I can consume relatively vast amounts of information fairly quickly. Plus years of experience doing this. However, reading fast has its perils as well so experience has taught me to go over papers more than once. A gap in time helps plug gaps as fresh eyes bring more value to the task.

I find this general approach very versatile so much so that I use it both for work and elsewhere. For e.g., my hometown of Chennai recently suffered unprecedented floods that marooned the city and relegated it to the medieval age in one stroke. Since I have family there, I spent many waking hours tracking the situation on the ground the best I could on the internet. The material I found doing this formed the basis of my blog post cataloging what happened, why and what it says about the body politic, The 2015 South Indian Floods: The Front Page News Story that Global News Media Wantonly Neglected by Tirumalai Kamala on TK Talk.

Using a similar approach to catalog, collate and bin my starting material (see screenshot below), the post started to shape itself into existence. Again, Command+F is an irreplaceable help. Using it to find keywords such as 'drain', 'police', 'military', 'NDRF', etc., helped me quickly shape a narrative that made sense to my understanding of the situation. Quickly scan, copy-paste the relevant passages, move on. Soon, my post was done. 

So there you have it, a broad brush overview of my approach to review writing. How the review/answer starts to shape itself is the most mysterious aspect of this process. This is where the individual's unique Masala (or alchemy) makes all the difference. A feeling for narrative, bolstering arguments with tangible, verifiable, sometimes testable data, one part of the narrative flowing to the next, these are some of the essential elements. Often arguments in one section will stoke into existence logical questions. These can then serve as bridges connecting one section to the next, or even one para to the next. In this manner, hopefully a cogent narrative emerges, akin to a building, the original database the foundation and the review sections the above-ground structure the foundation makes possible. More comprehensive the database (foundation) that went into researching the review topic, better the review (building) and greater its value.

https://www.quora.com/What-are-the-best-ways-to-write-a-literature-review/answer/Tirumalai-Kamala