I have outlined below what you should do. In short, yes it is possible, because I use it everyday
- Go to System Preferences → Keyboard → 'Shortcuts' tab.
- Click on the 'Mission Control' option in the left sidebar.
- Now on the right sidebar you will see a Mission Control heading with a disclosure triangle next to it. Click on the triangle to show additional options.
- You will see predefined options for you to select from; however, the keyboard shortcuts can be edited as necessary. I have mine set to Command-→ to switch between spaces.
If this doesn't work for you, it's because you don't have your displays segregated. If you're running more than one monitor:
- Go to System Settings > Mission Control and check 'Displays have separate Spaces'.
- You will have to log out and log back in for it to take effect.
Additionally, for further desktop organization you can set your apps to only appear on a certain window or space, so that way that application only populates in the space you designate. You can do this by going to System Preferences → Mission Control and check "Group windows by application" so there isn't cluttering of applications.
This is not OS specific (works with Mavericks or Yosemite) and is not prejudiced to full screen apps. In other words, since you're switching spaces it doesn't matter what's in the space or how it's displayed; it will switch regardless. Lastly, it functions regardless of your screen output, setup, or format. I have three monitors and it only affects the active display.