Apple has published a knowledge base article detailing steps for existing iPhone owners to take in upgrading to the iPhone 3G. Apple walks through the backup and restoration process which will require iTunes 7.7 for the iPhone 3G.
One new bit of information for U.S. customers is the fact that you will not move your existing iPhone SIM card to the new iPhone. Instead, the iPhone 3G's SIM card will be reprogrammed with your information:
In the US, iPhone 3G includes a SIM and your original iPhone's SIM is not needed. Your original iPhone account information will be transferred to iPhone 3G's included SIM when you purchase iPhone 3G. To dispose of your original iPhone SIM, contact your carrier.
For whatever reason, international users may simply use their original iPhone SIM card in the iPhone 3G.