This is done by ActiveSync which you have on the phone. However, you must have email, contacts hosted on a Microsoft Exchange Server. If you have a regular POP email account you can't do it.
Most people with Exchange Server accounts either have it because their employer does it, or they sign up for one and pay per most for Exchange Hosting (e.g., 123Together.com, etc.). I think there may be a few free Exchange Server offerings, but not sure who and how that works.
I understand that you may be able to get a Gmail account that does syncing of your contacts, calendar and email with the Droid, but someone else who knows if this is correct and, if so, how to do it will need to speak up.