From your home screen, hit MENU, then SETTINGS, then ACCOUNTS. You'll see your choices of various accounts (gmail, facebook, etc). If you click on the account, you'll see the choice of what it can sync, and at the bottom there is REMOVE ACCOUNT which will remove it from the device comletely. Since you said it's a second account, is it safe to assume it's not the one that all your apps are tied to?
