It is secure and easy to login into servers with openssh using public/private key client authentication. You only need to generate keys with ssh-keygen and these keys are used automatically.
Challenge starts when you dont want to use same key everywhere but prefer or have to use different keys for different sites.
Firstly lets create a few keys. Add also meaningful comments immediately that help you to remember which key was for what. ssh-keygen offers you choice what you want to have key names
$ ssh-keygen -C "my work key" $ ssh-keygen -C "personal stuff"
Now copy public key to remote into ~/.ssh/server authenticated_keys or ~/.ssh/authenticated_keys2 file.
Change ssh configuration. Either systemwide in /etc/ssh/ssh_config account basis in ~/.ssh/config. Write into this file where your private keys are and which hosts they apply to.
Host server.atwork.com IdentityFile ~/.ssh/id_rsa.work
Host personal.webserver.com IdentityFile ~/.ssh/id_rsa.personal
See also Setting up public key authentication