Windows 8 has a new screen when you start up which is called the Lock Screen. You can lock your pc, allowing yourself to remain signed in, with any currently running apps still running, and allowing others to log in. When you sign out (which was previously called "log out"), others can sign in. If you sign out, then any running apps are closed, but the pc remains running normally.
If you drag up on the Lock Screen with your finger (assuming you have a touch screen computer), or with your mouse if it's a normal laptop or desktop computer, the Lock Screen scrolls up and you can log in.
There are a couple of ways to log in: with a normal Local Account, or with what used to be called a Windows Live ID and is now called a Microsoft Account. There are other types of accounts that are used as Microsoft Accounts also, such as Microsoft Passport, and Microsoft Wallet. Microsoft Accounts can be used for Xbox Live, Windows Phone, and Zune. Most Microsoft Accounts will be associated with an email address from hotmail.com or live.com or outlook.com, but you can create a Microsoft Account that will be associated with any email address, such as for example gmail.com.
There are several differences between a Local Account and a Microsoft Account: a Local Account only gives you access to the pc you're on, none of your settings will be synced between the pcs you use and you won't get any benefits from connecting your pc to the Cloud; a Microsoft Account, on the other hand, will allow you to access services like Hotmail, Facebook, Twitter and LinkedIn; it will also sync your Windows 8 settings on multiple pcs that you log into; you can find options that control these settings in the PC Settings application -> Change PC settings -> Sync your settings. And you can acquire apps from the Windows Store and use them on any Windows 8 pc you sign into. (A Local Account can only browse the Windows Store.)
Some of the Windows Store apps only work with a Microsoft Account; these include the Calendar, Mail, Messaging, People and SkyDrive apps.
You can switch between a Local Account and a Windows Account in the PC Settings application. You use either the Switch to a local account or Switch to a Microsoft account button under your username in the Users -> Your account section of this app.
When you log out, you can do it by displaying the Start screen and then either tapping (for a touch screen) or clicking (with a mouse) the user name at the top right, and then choosing Lock on the menu that will appear. You can also type the Windows key (hereafter called the WinKey) and the L key. When you have the top right menu of the Start screen expanded, you can also choose "Sign out" from the menu. The difference between "Lock" and "Sign out" is a little ambivalent, since both will take you to the Lock screen. But "Sign out" will close any running applications, while "Lock" will not close them. In either case, another user can sign in. There is also an option for "Change account picture."
The image that appears below shows the Start screen with the menu that shows Lock and Sign out. (Note that I have made all the rectangles on the Start screen into squares, and then sorted them by pairs of columns into alphabetical order, except for the shortcuts to Shutdown and Restart that I added. I have also put labels above the different sections.)