To create the private and public keys type on the unix prompt:
$ ssh-keygen
You can use the default location, and not use a passphrase. The keys will be created in the directory:
/home/<username>/.ssh/
Inside this directory you’ll find two files id_rsa (the private key), and id_rsa.pub (the public key).
Login into the remote server and created the ‘.ssh’ under the home directory. Ensure the directory only has permissions to the owner.
$ ssh <remote username>@<remote hostname>
$ mkdir .ssh
$ chmod 700 .ssh
Go back to your host server and copy the public key to the remote server.
$ sftp <remote username>@<remote hostname>
$ put /home/<username>/.ssh/id_rsa.pub ./ssh
Login into the remote server again and rename the public key to authorized_keys. Also ensure the file only has permissions to the owner.
$ ssh <remote username>@<remote hostname>
$ cd .ssh
$ mv id_rsa.pub authorized_keys
$ chmod 600 authorized_keys
Next time you ssh to the remote server, you should be logged in automatically without needing to enter a password.