How do I log into a remote computer?

Use ssh
To avoid having to enter a password with ssh or scp use keychain.
Generate the keys (only needs doing once):
ssh-keygen
cp ~/.ssh/id_rsa.pub ~/.ssh/authorised.keys (scp to remote host if not same home dir)
Run keychain (/usr/bin/keychain)
After login,
source ~/.keychain/ -- this can be put in your .bashrc etc

Some old notes by ACI - and is wrong - is still available here.