In Ardour, work is done in two main windows: the Editor and the Mixer.
The Editor and the Mixer share the same toolbar (the top of the window). The sections displayed in this toolbar can be customized to the user's workflow, by checking options in Preferences > Appearance > Toolbar.
Switching between the Editor and the Mixer windows is done:
Both windows can be visible at the same time (e.g. for a multi-monitor setup) using Window > Editor (or Mixer) > Detach option in the same submenu.
The Editor window includes the editor track canvas where audio and MIDI data can be arranged along a timeline. This is the window where editing and arranging a project is done. The window has a general "horizontal" sense to it: the timeline flows from left to right, the playhead showing the current position in the session moves from left to right—the window really represents time in a fairly literal way.
It is possible to show a single channel strip in the editor window, and some people find this enough to work on mixing without actually opening the mixer window. Most of the time though, both of these windows will be needed at various stages of a session's lifetime.
The Mixer window represents signal flow and is the window that will probably be used most when mixing a session. It includes channel strips for each track and bus in the session. It has a general "vertical" sense to it: signals flow from the top of each channel strip through the processing elements in the strip to reach the output listed at the bottom.
To learn more about the process of mixing, see Mixing.