You can start by just trying to hook it back up after disconnecting the new one. If you do not receive an IP address, odds are Verizon has you registered for the MAC address (Hardware address) for the new modem. Just call up the customer support and tell them you would like to go back to your old modem, and they will ask for the MAC address if they don't still have it on file, or the serial number off the bottom of the modem.
Verizon is usually pretty good about prompt service, at least in my area. If you call back and ask to speak with a manager, explain the situation and perhaps you will either get someone out there ASAP or some $$ off the bill for the inconvenience.