Q:

how to configure open ldap to work on localhost

From the documentation:

Use your favorite editor to edit the
  provided slapd.conf(5) example
  (usually installed as
  /usr/local/etc/openldap/slapd.conf) to
  contain a BDB database definition of
  the form:
  database bdb
  suffix "dc=<MY-DOMAIN>,dc=<COM>"
  rootdn "cn=Manager,dc=<MY-DOMAIN>,dc=<COM>"
  rootpw secret
  directory /usr/local/var/openldap-data

But, my domain is either 127.0.1.1 or localhost,
What should I put instead of MY-DOMAIN and in COM ?

A:

You can put whatever you want. Suffix has nothing to do with what IPs/interfaces slapd listens on. Suffix is the top level of the data tree, it doesn't have to be DNS/network names.  Think of it as your database name.  So while you could use:
suffix "dc=localhost,dc=localdomain"
or 
suffix "dc=example,dc=com"
you could also use:
suffix "dc=my,dc=ldap"
You can have more than two parts if you want
suffix "dc=my,dc=ldap,dc=server"

