This how to setup public key authentication over SSH :

1. Generate key on local machine

ssh-keygen -t rsa

or

ssh-keygen -t dsa

2. Choose a passord

It will ask you a password, you can type one or leave it blank.

3. Copy your key to the remote server

Make sure the server your connecting to has a .ssh directory in the home directory. If it doesn't exist you can run the ssh-keygen command on the remote server. Copy your local public key located in the file ~/.ssh/id_rsa.pub to the remote server at the end of the file ~/.ssh/authorized_keys

Now you can ssh to the remote server without typing your password.