What exactly are you talking about? Do you mean your GMail account? The Nook Color will only access the Internet via WiFi, so if you don't have a router you are out of luck as far as that goes unless you have a free hotspot nearby.
If you're talking about your Google account for the Android Market, use your Google email address when you register your Nook with B&N. Then, when you create your Market account use the same email address. As Sue said, you're going to need a WiFi router to access your own internet account.