To use ssh between hosts without a password:

First, on host1 you need to make sure that a directory called .ssh exists in the user's home directory (we'll assume root). To keep it secure, create it with 700 permissions:

mkdir -m 700 .ssh

Then you need to generate a public/private key pair:

ssh-keygen -t dsa -f ~/.ssh/id_dsa

Enter a blank passphrase (twice).

Now copy the public key to host2:

cd .ssh
scp id_dsa.pub root@host2:~/.ssh/id_dsa.tmp
(You still need to supply the password at this point)

Now on host2, add that public key to the list of authorised keys:

ssh host2
(Password still needed)
cd .ssh
cat id_dsa.tmp >> authorized_keys
(Note American spelling!!! "authorized" with a zed)
chmod 640 authorized_keys

root on host1 can now login to host2 without a password.

To get this working in both directions (i.e. root on host2 can also log in to host1 without a password), you basically do the same thing in reverse: Create a public key on host2 and copy it to host1.
NOTE: Do not overwrite the original id_dsa.pub file, or you will have un-done all of the above. Also, do not overwrite the authorized_keys file: just append to it with ">>".

Basically the key in id_dsa.pub on the local host must match an entry in the authorized_keys file on the remote host for the password to be skipped. The authorized_keys file can contain several entries. Just keep appending to it as shown above.