Generate key on local machine
ssh-keygen -t rsa
It will ask you for a password but you can leave it blank.
Note you could also pick -t dsa if you prefer. Ensure that the remote server has a .ssh directory
Make sure the server your connecting to has a .ssh directory in your home directory. If it doesn’t exist you can run the ssh-keygen command above, and it will create one with the correct permissions. Copy your local public key to the remote server
If your remote server doesn’t have a file called ~/.ssh/authorized_keys then we can create it. If that file already exists, you need to append to it instead of overwriting it, which the command below would do:
scp ~/.ssh/id_rsa.pub remote.server.com:.ssh/authorized_keys
Now ssh to the remote server
Now you can ssh to the remote server without entering your password.
Security
If you are unable to login without being prompted for a password it is likely the result of improper permissions being set on .ssh/ and its children. SSH is picky about permissions; to fix the problem, ssh to the remote server and issue the following command:
chmod -R 700 .ssh/
Now keep in mind that all someone needs to login to the remote server, is the file on your local machine ~/.ssh/id_rsa, so make sure it is secure.