Question: I know that it is required to first create a database of references stored in a `.bib` file. Mendeley exports my reference list in `.bib` format. But how can I know what to write in curly brackets in `\cite{}` to refer to a particular author? Do I need to keep the `.bib` file open and find the relevant name to cite? Or am I missing something? What is your recommendation for referencing in LaTeX?

Answer: 
You have several options here. One is, as you suggest, to simply keep the `.bib` file open in the text editor and search for the cite key as you need it. Another is to use some software such as JabRef or BibDesk to manage the `.bib` file, which will be somewhat complicated since Mendeley overwrites the auto-generated `.bib` file every time a reference is updated.

Thus, I prefer to use the better searching capabilities of Mendeley, so I usually look up the citation key there. Unfortunately, Mendeley have decided that citation keys should not be visible by default, so you have to turn them on. Here I'll copy from my answer to [a different question](https://tex.stackexchange.com/a/173034/32374): Go to the menu->Tools->Options->Document Details, then choose the document type (for instance, Journal Article), then check the Citation Key box. Then, a field for Citation Key should be visible in the details pane on the right hand side of the window.

![Options Box](https://i.stack.imgur.com/XW1iu.png)
![Document Pane](https://i.stack.imgur.com/QFgNp.png)
Another simple way is to select the file in Mendeley list, then right-click and select "copy as", then "LaTex citation command" (which corresponds to ctrl+K), and last paste the thing inside the brackets of \cite{}