.bib file, then cite from it as usual. The file is a copy: it changes only when you click Refresh.
Link your Mendeley account
You do this once.Open your account settings

Mendeley in the account settings

The Integrations panel
Authorize on Mendeley
Check the link

Your Mendeley account is linked
Create a file from your library
Open the Add files dialog
Choose the file name and the library
mendeley.bib. Keep the .bib ending: without it you get no preview, and neither \cite nor \bibliography finds its entries.Library starts as My Library, and also lists your groups. One file holds one library.
A file from your personal library
Click Create

The imported file
Import a group
Do the same again, with a file name of its own, and choose the group under Library. A project can have several of these files.
A file from a group
Cite from the file
Start a citation
.tex file, type \cite{. The list shows the entries of all the .bib files in the project. Click one to insert it.
The entries of the imported files
Or search by title or author

The reference search
Add the bibliography
\end{document}, using the name of your file without .bib. For several files, separate the names with commas.
The compiled reference
.bib file. You can still cite from them.

The empty list is expected
Refresh the file
Changes in your Mendeley library do not reach the project on their own.Open the file
Click Refresh

The refreshed file
Recompile
Unlink your Mendeley account
In Account settings, under Mendeley, click Unlink, then Unlink again in the dialog. The button says Link to Mendeley again.
Unlink your account

Refreshing without a linked account
If something goes wrong
Could not load references from Mendeley, please re-link your account and try again, or There was an error accessing your Mendeley data in the Add files dialog: Overleaf can no longer read your library, for example because you removed its access on Mendeley. In Account settings, click Unlink, then Link to Mendeley. Create also fails until then, with the message The project that contains this file is not shared with you, even in your own project.
Overleaf can no longer read your library

