Generate the ssh keypair

Run the ssh-keygen program on the command line and press ENTER on every question:

$ ssh-keygen

More or less this is the expected output: (assuming your username is foo and your home directory is /home/foo.)

Generating public/private rsa key pair.
Enter file in which to save the key (/home/foo/.ssh/id_rsa):
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /home/foo/.ssh/id_rsa.
Your public key has been saved in /home/foo/.ssh/id_rsa.pub.
The key fingerprint is:
SHA256:CL+xpn2DJx4P3xddsCWAN2thkFIHKFp9kBr6NHf44Pw foo@ubuntu-ansible
The key's randomart image is:
+---[RSA 2048]----+
|       ..=+=o.   |
|      + = +.= o .|
|    .+ + + o + = |
|    oo+.+ . o . .|
|     o+=S+ . . . |
|      .+o . . .  |
|      *. .   .   |
|     +o=+.E .    |
|    ..o+o...     |
+----[SHA256]-----+

This generates two files: ~/.ssh/id_rsa is the private key. You need to keep it super-safe. ~/.ssh/id_rsa.pub is the public key. This you can distribute to anyone. You can even advertise it on your site. One, theoretically, cannot compute the private key based on the public key in any reasonable time.

Deploy the public key

Basically you need to take the content of ~/.ssh/id_rsa.pub on the manager machine and append it to the content of ~/.ssh/authorized_keys and make sure both the ~/.ssh directory and the ~/.ssh/authorized_keys file has very restricted rights allocated:

drwx------ 2 foo foo ... .ssh/
-rw------- 1 foo foo ... .ssh/authorized_keys

Luckily you don't need to do it manually as there is a command called ssh-copy-id that will do all of that on your behalf. Of course it will ask you to type in the password of the remote machine as it needs to log-in once before it copied the public key, but then it creates the necessary directory and file if necessary and appends the new public key. We just need to provide the IP address of the remote server.

ssh-copy-id 192.168.56.11

The output looks like this:

/usr/bin/ssh-copy-id: INFO: Source of key(s) to be installed: "/home/foo/.ssh/id_rsa.pub"
/usr/bin/ssh-copy-id: INFO: attempting to log in with the new key(s), to filter out any that are already installed
/usr/bin/ssh-copy-id: INFO: 1 key(s) remain to be installed -- if you are prompted now it is to install the new keys
foo@192.168.56.11's password:

Number of key(s) added: 1

Now try logging into the machine, with:   "ssh '192.168.56.11'"
and check to make sure that only the key(s) you wanted were added.

Then you can ssh to the remote machine without providing a password.

$ ssh 192.168.56.11