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_keys2 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_keys2

Now ssh to the remote server

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

Security

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.