Bash Toolkit | Your Swiss Army Knife for the Command Line

Generate ssh-key

ssh-keygen -t rsa

Generating public/private rsa key pair.
Enter file in which to save the key (/home/user/.ssh/id_rsa):
Created directory '/home/user/.ssh'.
Enter passphrase (empty for no passphrase):

After that you will see public key :

Your public key has been saved in /home/user/.ssh/id_rsa.pub
The key fingerprint is: ...

copy fingerprint and paste into:

vim /home/user_remote/.ssh/authorized_keys

and than you will connect via ssh without password but if you entered passphrase, system will ask you this.