With version 1.0 of Gmail on the iPhone, you were able sign in and out of an account by scrolling to the bottom of your inbox. With version 2.0's infinitely scrolling inbox, you'll need to look elsewhere to sign in and add multiple accounts.
If you previously used the Gmail app and updated to version 2.0, you'll still be signed in to your account. To add up to four additional accounts, tap the menu button in the upper-left corner or swipe right to reveal Gmail's menu. Next, tap the button at the top of the menu with your profile picture, e-mail address, and downward arrow. A new menu will slide into place, with a large button to "Add account." You can then use this menu to switch among your various accounts.
Unfortunately, there is no universal inbox feature that lets you view mail from all of your accounts on one screen. Also unfortunate is that you can't sign out of an individual account; there is a button that signs you out of all accounts at the bottom of the add accounts menu, but I could not find a way to sign out of just one of my accounts.