Screen Sharing is a service built into OS that allows a Mac to be controlled by another device (a PC, iPhone, iPad, etc.) It was officially introduced in Leopard, though the ability to VNC into a machine goes back long before that. It was Leopard that brought the actual Screen Sharing application.
Until Lion, you would connect to a Mac and see whatever was on the screen of the Mac. So, if someone else was using the machine, you would see what they were doing and you'd each have the ability to controll the mouse and type keyboard commands.
Lion introduced Per-User screen sharing. This allows you to "remotely log in to a Mac with any user account on that computer and control it, without interrupting someone else who might be using the computer under a different login."
This change is incredibly useful but there is a slight limitation. As found by AFP548.com in the Lion Eula:
Section 2,H. Remote Desktop Connections. Subject to the terms and conditions of this License, when remotely connecting from another computer or electronic device (each a “Device”) to an Apple-branded computer that is running the Apple Software (for purposes of this Section, such Apple-branded computer is referred to as the “Home Mac”), whether through the Screen Sharing feature or through any other means:
(i) only one (1) Device may remotely connect at any one time, whether directly or indirectly, to control the graphical desktop session of the Apple Software that is running and being displayed on the Home Mac; and
(ii) a reasonable number of Devices may remotely connect at the same time for the sole purpose of simultaneously observing the same graphical desktop session of the Apple Software that is running and being displayed on the Home Mac, as long as they do not control the Apple Software in any way; but
(iii) only one (1) Apple-branded Device may remotely connect at any one time, whether directly or indirectly, to control a separate graphical desktop session of the Apple Software that is different from the one running and being displayed on the Home Mac, and such connection may only be made through the Screen Sharing feature of the Apple Software.
Except as expressly permitted in this Section 2H, or except as otherwise licensed by Apple, you agree not to use the Apple Software in connection with service bureau, time-sharing, terminal sharing or other similar types of services. You also agree not to use or offer the Apple Software, or any of its functionality, to provide service bureau, time-sharing, terminal sharing or other similar types of services to third parties.
Or in other words, if someone else needs to control the same Mac that you are using then only one device can do it at a time. That's a letdown but I can understand that it is a move to preserve Mac sales.
Now that the use limitations are clear, what is the actual process of Screen Sharing?
First, be sure to enable Screen Sharing on the server. It is found in System Preferences -> Sharing
Now from the client end, just use the Finder menubar Go -> Connect to Server (or Command+K)
When Screen Sharing finds the server, you'll enter the user login for the remote Mac and then you'll see the screen as if it's sitting in front of you. The screen you see will depend on what authentication you use to connect.
The actual Screen Sharing app is also improved. It now offers " a new toolbar that provides access to useful tools and settings such as screen resolution, Clipboard access, and screen capture." (For a tip, the first time you connect with Screen Sharing, right-click the app in your dock and choose to "Keep In Dock." With it there, you can click on it much quicker without the "Go To Server")
Lion brought great news for iPhone screen sharing clients because you no longer have to enable the "VNC" option in Screen Sharing. And even better, you'll be able to log right into your user account (instead of first seeing the OS X login screen which happened with VNC.)
When you setup a new machine in either of these apps. You'll be asked the regular information (machine name, address, etc). Then, as part of the authentication you can choose the new option "Mac" and enter your OS X user and password. This will bring you right to your desktop.
So in summary, the Screen Sharing to Lion has been vastly improved. It's easier to connect from both iOS devices and Macs…even though you can only connect from one at a time. (At least according to the EULA)