One of the new features of Exchange 2010 is Federation. It allows companies to share exchange related data with external companies such as Free/Busy and contacts.
In previous versions of Exchange you would have to create a forest trust between the organisations and use the Inter-Org Replication Tool for replicating public folders and Identity Integration Feature Pack (IIFP) for replicating contacts.
I was going to spend some time writing an article on how to configure this however someone already beat me to the chase. I just read a fantastic article by Steve Goodman which runs through through each of the steps in making Exchange 2010 federation work.
Please have a read, here is the link to his blog site: