To display mission control, the trackpad shortcut is a four fingers swipe up (or three fingers according to the system preferences you set for your trackpad).
You can also hit the F3 key (without pressing 'fn' key) to display mission control.
Then, you should see all your windows. If you bring your mouse curser in the upper right coin of your screen, you should see a small rectangle with + sign: clicking on it will create a space.
If you want to go from a space to another, you can use ctrl+left/right, but you can also use your trackpad with four fingers swipe left/right (or three fingers).
You can configure the way Mission Control is brought to front in your System Preferences > Mission Control or Trackpad sections.
If all of this does not work, then you may have another problem.