Let user@ServerA be the host that wants to connect to user@ServerB.

Run the following commands as user@ServerA

ssh-keygen -t rsa          # use empty pass phrase, save the keys to ~/.ssh/id_rsa and ~/.ssh/id_rsa.pub
chmod 700 ~/.ssh           # set the permissions of the .ssh directory to 700.
chmod 600 ~/.ssh/*         # set the permissions of the keys so no one else can read them.

It’s important to set the permissions! Otherwise SSH will not use the keys without a warning or message. I’ve wasted enough time to learn this the hard way.

Copy the ~/.ssh/id_rsa.pub from user@ServerA to user@ServerB:~/.ssh/authorized_keys. Again, set the permissions.

chmod 700 ~/.ssh         # set the permissions of the .ssh directory to 700.
chmod 600 ~/.ssh/*       # set the permissions of the keys so no one else can read them.