The documentation mentions that the user or roles needs to have the 'find' action allowed, or to use the 'backup' role:
https://docs.mongodb.com/manual/reference/program/mongodump/#required-access
Login to your server - root via putty or SSH
The 'backup' role would need to be granted to any non-admin users, but it seems it's not needed for the main admin user I setup and I was able to use the following:
mongodump -u "admin" --authenticationDatabase "admin"
This will prompt the password and once you enter the BACKUP dump is created in the server...
A new directory named "dump" in working directory path and looks to have dumped all databases into it. This is currently at /root/dump/ as an example of what it contains, and more examples of using the command can be seen on https://docs.mongodb.com/manual/reference/program/mongodump/#mongodump-with-access-control
If you want to take the Backup individually then use the following process:
The --db flag can be added to specify just one or a few databases, and --out flag can be added to specify an output directory, so if you instead wanted to create the dumps of all databases in a specific directory (/backup/mongodumps for example) you would do something like the following:
mongodump -u "admin" --authenticationDatabase "admin" --out /backup/mongodumps/
or if you just wanted one database to a specifc directory:
mongodump -u "admin" --authenticationDatabase "admin" --db [DB name] --out /backup/mongodumps/
There are also other examples at https://docs.mongodb.com/manual/reference/program/mongodump/#mongodump-with-access-control which include compressing the dumps, or dumping them to a single archive.
Additional info:
Otherwise if you want to create dumps as a user other than admin, then the 'backup' role will need to be granted to those other users.