Spaces first appeared in OS X Leopard, but in Lion, the feature has been rebranded, along with Expose, into the new Mission Control feature. Mission Control is your one-stop place for viewing all of the opened application windows on your Mac, full screen apps and. Dashboard widgets. It also lets you create multiple desktops, which enables you to organize your windows by the types of applications or by the work you’ll do in each Space. For instance, you can have a Desktop for work that has your email client, web browser, or other work related applications.
You can create up to 18 (!!!) separate Desktops in Lion. This includes full screen applications, the Dashboard space, and additional desktops.
There are three different ways to create Desktops. The first is to enable full screen mode from the right-hand corner of the title bar.
When you do this, a new Desktop will be created in mission control for the full screen application. All full screen applications get their own Space.
Another way to create a space is by hovering over the top left or right of the Mission Control screen until you see a Desktop with a plus button on the top of it. Clicking on this will create a new Desktop within Mission Control. 
The final way to create a new Desktop is by dragging and dropping an opened window from the Mission Control section to the top left or right corner until this Desktop icon appears. This automatically creates a new Desktop and places that window there.
If you have created too many different Desktops to keep track of, just hover over the top left of the Desktop in Mission Control and click on the “X” button that appears. Any windows contained in a closed Desktop will be moved to the first Desktop.
To move windows between spaces, simply switch to the one you’d like to move a window from by clicking on the Desktop in Mission Control, and then dragging and dropping the window onto the Desktop you would like to move the window to.
You can have certain windows always open in certain Desktops. To do this, navigate to the Desktop you’d like the application to open in and right-click on the application in the Dock and navigate to Options > This Desktop. You can also have the application be available to All Desktops or select the default of None.
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jhbrewer
December 14, 2012 at 1:40pm
Aha! The ^# method for jumping to the desired desktop (#) still exists; it is simply buried in a less-than-obvious place: under System Preferences -> Keyboard -> Keyboard Shortcuts -> Mission Control where you just have to check the boxes for "Switch to Desktop #". I never would have found that without the help of a friendly AppleCare tech. Now it behaves the way it used to under Snow Leopard and I am happy again.
ivantsy
September 07, 2012 at 7:13pm
Ctrl + 1, Ctrl + 2 etc. will switch to different display (desktop).
bangaboomerang
July 10, 2012 at 9:07am
Any way to arrange it in 'rows and columns' like before ?
Navigating left and right only is not practical. . . . .
jhbrewer
June 01, 2012 at 10:13am
I insist upon quick and convenient switching between desktops ("Spaces") where specific applications always run; otherwise I might as well be running Windoze with everything piled up in a jumble on one desktop. Under Snow Leopard this was easily managed by setting an unique keystroke to each Space. Now I have to first click on Mission Control and then hunt for the right Space using the mouse. I have looked in Mission Control System Preferences for a way to assign a keystroke code for each Space, but nothing there seems to address this issue. Do I have to downgrade back to Snow Leopard to restore an ergonomic interface?
ZD26
July 20, 2011 at 1:52pm
I'm finding that apps are not very cooperative at opening up in their assigned spaces, especially if that Desktop number is not open. I'll explain further: I am (was) a hardcore Spaces user, and liked certain apps to open in certain Spaces. Now, they just won't. For example, I like iTunes to open in Desktop 4. So I create 3 additional desktops (final one being number 4) and open iTunes, and use the trick you described where you right-click the iTunes dock icon, and set Options>This Desktop. However, if I quit out of iTunes and close Desktops 2, 3, and 4, I when I try to open iTunes again it just opens in Desktop 1… this is WRONG! Either Apple decided to screw over its serious Spaces users or this is a major oversight (and Spaces feels like an afterthought to Expose anyways). Any insight?
stephenjames716
October 26, 2011 at 7:16am
Hi, I was having the same problem and found this on an apple discussion thread:
Lion automatically orders Desktops and full screen apps by the most frequently, and recently used. This is why they are switching.
To stop this, go to System Preferences, then click Mission Control and untick 'Automatically rearrange spaces based on most recent use'.
Brunno
July 20, 2011 at 4:00pm
Your issue is easily solved: the same way you would not close/erase different Spaces on Snow Leopard, don't close the various Desktops on Lion.
I was used to having 6 Spaces on SL and jump between apps using the four finger side swipe and it worked like a charm, jumping from app to app and Space to Space, depending on where there were being used (some apps were preset just like yours).
The four-finger side swipe was ditched now, and can only be accessed using CMD+Tab.
Snarkicist
July 20, 2011 at 11:20am
I have a 24" iMac connected to a 19" HP monitor. I use a lot of apps simultaneously, reviewing docs in Preview, accessing databases in Safari with multiple tabs, taking notes in Excel, and pulling other reports from a USB drive via Finder.
In other spaces, I have Mail on one monitor and Safari on the other; in another space, I have iTunes running, and my 4th space is for when I need something else, like the App Store or Angry Birds.
I'm curious to see how this will work in Lion. Any advice would be greatly appreciated.
