From your words, I think that what you want is to configure a feature commonly called Outlook Anywhere.
This feature allows any internet connected outlook to sync a user account with an Exchange Server directly without need a prior VPN connection.
You did not give many details, but for this to work, there are several steps to take into consideration. Not only to securely “publish” this service but also in terms of the overall environment configuration.
If all the this service is already configured on your network and you just want to know how to configure your Outlook, please take a look at this article.
If you want more than this, please give us more details.