I've already written about howto log in, on your local system, and make passwordless ssh connections using ssh-keygen command. However, you cannot just follow these instructions over and over again, as you will overwrite the previous keys.
It is also possible to upload multiple public keys to your remote server, allowing one or more users to log in without a password from different computers.
Step # 1: Generate first ssh key
Type the following command to generate your first public and private key on a local workstation. Next provide the required input or accept the defaults. Please do not change the filename and directory location.
workstation#1 $ ssh-keygen -t rsa
Finally, copy your public key to your remote server using scp
workstation#1 $ scp ~/.ssh/id_rsa.pub email@example.com:.ssh/authorized_keys
Step # 2: Generate next/multiple ssh key
a) Login to 2nd workstation
b) Download original the authorized_keys file from remote server using scp:
workstation#2 $ scp firstname.lastname@example.org:.ssh/authorized_keys ~/.ssh
c) Now create the new pub/private key:
workstation#2 $ ssh-keygen -t rsa
d) Now you have new public key. APPEND this key to the downloaded authorized_keys file using cat command:
workstation#2 $ cat ~/.ssh/id_rsa.pub >> ~/.ssh/authorized_keys
e) Finally upload authorized_keys to remote server again:
workstation#2 $ scp ~/.ssh/authorized_keys email@example.com:.ssh/
You can repeat step #2 for each user or workstations for remote server.
Step #3: Test your setup
Now try to login from Workstation #1, #2 and so on to remote server. You should not be asked for a password:
workstation#1 $ ssh firstname.lastname@example.org
workstation#2 $ ssh email@example.com
Updated for accuracy.