How to set-up SSH to not require a password every time you log into a remote machine.

Have a look at this nice how-to:
http://www.astro.caltech.edu/~mbonati/WIRC/manual/DATARED/setting_up_no-password_ssh.html

I.e. in short:

On local side:
ssh-keygen -t dsa -f .ssh/id_dsa
cd .ssh
scp id_dsa.pub user@remote:~/.ssh/id_dsa.pub
ssh user@remote

On remote side:
cd .ssh
cat id_dsa.pub >> authorized_keys2
chmod 640 authorized_keys2
rm id_dsa.pub
exit

On a new account on the server, you might also first want to run:
remote> ssh-keygen -t dsa

This will help create the .ssh directory on the server that might otherwise be missing, and set the attributes correctly (having the directory attributes wrong is otherwise a cause of error, chaos & confusion).