Check out Mission Control on your Dock. If it is not in your Dock, then look in Applications -> Mission Control
When Mission Control shows all the windows on your desktop, if you move your mouse to the upper right side of the screen, a + will appear. Click the + and a new space will be created.
In the Mission Control display the top of the screen shows you all your spaces.
System Preferences -> Mission Control will allow you to configure the hotkeys that will switch between spaces. Default is Control-up-arrow Control-down-arrow.