Very simple, install mod_auth_ldap, and then install a .htaccess file that looks like this:
AuthType Basic AuthName DDInternal AuthLDAPURL ldap://yourzimbraserver/dc=zimbra,dc=yourdomain,dc=com,dc=au require valid-user
The first part "ytourzimbraserver" is the address of your Zimbra server running LDAP.
The second part "dc=zimbra,dc=yourdomain,dc=com,dc=au" is the domain you would like to authenticate against.
I am not sure at this stage if you can allow users from multiple domains. Ideally the login would be the same form as Zimbra login - ie: "user@domain"
You may consider installing mod_ldap to cache your LDAP connections.
You can then use [Preauth] to do single sign on (sort of).